When you observe the full moon from the Northern Hemisphere, yo see the moon one way. When you are in the Southern Hemisphere, you see it upside down. When you are on the equator, how does it appear?
It depends which way you lean back your head.
Imma go out on a limb here and say: Halfway round from its Northern Hemisphere aspect to its Southern, if you’re looking at it low enough in the sky not to need to lean your head back.
A helpful image. Want to guess how I found it?
It depends on your orientation and when you look. Let’s pick an example. Suppose you look when the moon is highest in the sky, about halfway between moonrise and moonset. For convenience, let’s assume we are near the equinox and the moon is directly over the equator. Looking from the northern hemisphere, it will be most convenient to stand with your back to the north and looking south. Of course, you could stand the opposite way and lean your head back, but that is a bit awkward. From the southern hemisphere, you’ll likely stand the other way, looking north. The moon will be inverted. From the equator, you’ll look straight up and you can face any direction you like. A different way to view the moon would be to lie on your back and look up. You are now free to turn your body any way you like and see the moon in whatever orientation you prefer in either hemisphere.