You might try walking by their house on a good gardening-weather day. That way, you might see them outside, and then you could ask them without knocking. It worked for me. The lady even offered me a cutting (or whatever the word is–I’m not much of a gardener) of the flowers I was interested in, which turned out to be evening primroses.
PS. Maybe the 8" pink flowering perennials are creeping phlox?
Knock on door.
Say “I’m sorry to bother you, but I drive past your house every day and I absolutely love the shrubs in your garden and would like to get some for my own garden. I’m wondering if you know what they are?”
If they know, they tell you and maybe have a chat to you about how hardy they are, what maintenance is needed, etc. You thank them for the information, then leave.
If they don’t know, you then say ‘Would you mind if I took a photo of one of the flowers to take to a garden center?’ If they don’t mind, you take the photo, say thank you very much and leave.
If they do mind, you apologize for bothering them, wish them a pleasant evening and leave.
I’m going to echo everyone else’s comments, knock on the door. Most people who maintain a well landscaped lawn are fairly proud of it. Being complimented will feed into that ego and gives them an opportunity to talk about the plants which they probably love to do. I have a very nicely landscaped home and I’ve spent a lot of time on it over the years getting it to where it is now. It makes my day every time someone walking by the house while I’m outside stops to give me a compliment on the landscaping.
Now, in the next month I’ll be moving to a new home we’re buying and it has shit for landscaping so I get to start all over again! I’ll miss my current yard but starting a new project to bring beauty to the outside of the home that everyone passing by can enjoy is kinda exciting to me!
When I see a garden I particularly admire I have been known drive/walk pass on a regular basis hoping to see the gardener in the yard, then I will stop and get out to talk with them. On two seperate occasions I have had particularly delightful results; once there was a house in the next town over from where I used to live (and live now) and the backyard was filled with dahlias of every color and variety. When I introduced myself to the woman she took me on a tour, describing the dahlias and cutting me a huge boquet which she gave me gratis, even though I offered to pay her for it. While living in Kodiak, Ak. there was a very old woman who maintained a beautiful garden filled with perennials she had tended for many, many years. I stopped and spoke with her for about an hour, she was delightful and I learned some great tips for gardening in Alaska. I am so glad that I stopped, as she passed away the following winter and her house was sold and the garden went to hell.
While living in Kodiak I had a penchant for growing things the garden club told me could not be grown there. So when I had a towering stargazer lily with over 25 blossoms on it, and over 400 tulips and other spring bulbs blooming in July it pleased me to no end when people would pass the house, stop, back up and pull into the driveway for a better look. If I wasn’t out in the yard grubbing in the garden there was generally a kid outside who would run in and let me know the flowers had a visitor and I would go out and chat. Kodiak being such a small town I never minded, and I would like to think I wouldn’t mind here. Getting a note in the mail would be kind of creepy, I would probably not respond to that, and I might even call the p.d. to see if it was a scam going around.
Ok, let’s see if this works!
https://dumpyourphoto.com/photo/F38HlaH6p7
IT WORKS!! IT WORKS!!! (And there was much rejoicing! :D)
lieu, Thank you so very much!
It is not a flower picture. I just picked one from my phone to see if I could figure it out.
That is Little Man. He is telling me, “You will NOT read. You will pet me. NOW!”
It actually is not a potted plant, they’re in one of those black plastic 4-packs for planting. He wouldn’t have noticed if it didn’t have a tag, and I don’t think he realizes how varied they are. He knows I know they are tulips. He doesn’t know (or care, I guess,) about the names of the plants in the house, much less what’s in the flower bed outside. I’ve had to tell him repetitively which one is the bromeliad, the amaryllis, and others. The only houseplants he can identify are the jade, and the spider plants. He insists on calling the snake plant a “snake tongue.” 
He’s one of those people that when he goes to the store, he’s there to get what he wants and get out. (Unless it’s grocery shopping. He LOVES grocery shopping, and insists on going down every aisle, whether we need anything from that aisle, or not. Weird.) I’m truly surprised he thought to get them at all, they probably were not “on the list.”
No, these have bigger flowers and a pale pink color. 
I have decided that if the flowers/shrubs are close enough to the sidewalk that I can get a decent picture, I’ll post them here, so that Cat Whisperer can look at them!! 
I don’t know… it’s hard to read tone into text, but it seems like she’s eager to see them. It makes me happy. 
I can’t see myself walking up into someone’s yard and taking pictures without an explanation of some sort (now that would be creepy,) so I might knock on a few doors, and then ask to take the picture if they don’t know, as has been suggested.
Thanks all!
I think either approach is fine and the letter is more respectful and less invasive. But I see I’m outnumbered.
I would indeed like to see them - I like to see other people’s yards and plants.
I don’t walk into people’s yards, but I take pictures of their yards from the sidewalk all the time for my own research purposes - I archive the pictures for future gardening ideas. You get a lot more comfortable doing it after a while, and I have never had anyone have a problem with it. If someone came out while I was taking a picture, I’d tell them how much I liked their yard and I was taking a picture of their lovely double-flowering plum or whatever.
I am also eager to see them!
Cat Whisperer and TruCelt, I will post pictures for both of you! 
One more question… since I consider it a “less than cosmic” topic, would I post a “Can you name these flowers/shrubs?” thread here? Or would gardening questions technically go in the Café Society?
Good question - I’d say IMHO or MPSIMS, but the moderators might disagree.
I will echo MeanJoe. Anyone who has spent time making their landscaping look good gets stroked when someone (face-to-face) compliments their effort. Knock on the door. I bet you’ll get garden TMI from the gardener.
I would forget this one. I was in a similar case, years back. Still haven’t seen any signs of life from the house.
Glad to see that gardening is something to share here and I truly do hope the OP posts pictures. Still keep in mind that once you have a good picture, if we can’t help you (or if they are very esoteric) that showing the pictures at a local hot-house of plant store might help too.
I usually stalk the gardener til I catch them outside, then stop and compliment the garden and ask the name of that beautiful flower. Sometimes this method will result in a free plant or two. Perennial growers in particular are usually glad to divide a plant and give you a start.
What** papergirl **said.
My mom is that lady with all the flowers in her yard. The cars slow down as they pass, to get a better look and people often pull up to the curb to comment. She is very old now but somehow manages to manuver her walker around the flower beds on nice days, planting and pulling weeds. A stanger knocking at her door would freak her out, if she even heard you. Better would be just pulling up in front one day when she is out, compliment what you like and let that hang in the air for a moment - you’ll have more cuttings and advice than you can carry.
Stop being smarter than me.
I am going to post a picture, partly because I do want to know what this is, and partly because I am still trying to figure out the range necessary to identify a plant. This is a fairly close picture of a bush in my yard. I took another picture at a range of about 6 feet - but it is very fuzzy, and just looks like “green bush with white flowers,” no detail on the leaves or flowers themselves. If it helps any, the flowers smell wonderful, and in the fall/winter, it gets tiny bluish-black berries that the birds seem to love.
I have picked the berries and used them when I make home-made suet to feed the birds, but I really want to know… are they edible? It reminds me of a berry we picked at my grandfather’s, but that was many years ago.