Reversed order causing reversed meaning?

Is there a term for when reversing the order of words reverses the meaning?
For example: “Commercial free” vs. “free commercial”.

An antimetabole?

Depends on what you mean by “reverse meaning”. For instance, “Bob hit Frank” has a very different meaning from “Frank hit Bob”.

I suppose if you want a perfect reversal, you could go with something like “Eight exceeds six”.

D’oh, I thought you wanted examples, not a name for the phenomenon. Never mind me, then.

I mean simple two-word orders, which would be rarer.

That doesn’t actually reverse the meaning. “Commercial free” would describe (e.g.) a TV program that had no commercials, while “free commercial” would be an advertisement you didn’t have to pay for.

It is very common for reversing the order of words to change the meaning, but not reverse it; a well-known example is “house cat” vs. “cat house.”

I thought of it as “less commercials” vs. “more commercials”.

That’s not how I would interpret those phrases. In the first one, “commercial free” is acting as an adjectival phrase to modify an unstated noun. (As such, it should actually be a compound adjective “commercial-free.”) In the second one, “free” is acting as an adjective to modify the noun “commercial.”

(never mind)

Another way for it to occur is by having two nouns that can also be adjectives.
Liquid petroleum gas is the classic oxymoron.
Reverse the order, you’ve got the reverse case, gas petroleum liqid. That would be gasolense heated up to be a vapour.
I wouldn’t think there would be a term for such order reversals generally, because we can clearly reverse order for so many reasons. The quick red fox is the same as the red quick fox, you don’t need a reason.

But reversing two adjectics can change the meaning… An american african man is not an african american man. Its a sort of opposite, and could a stronger sort of opposite if there is some context to define “opposite”.
eg america was at war with africa …thats a context which defines opposites as opponents… enemies in the war

Relevant poem, containing several examples: The Lost Generation