this one is objective, the correct answer is 15/15.
you can claim there are twelve, but that claim doesn't hold up once we start investigating.
in order for the 12/12 answer to hold up you'd need to prove the non-existence of the enharmonic keys... problem is... they clearly exist.
yes, on tempered instruments they sound "the same." but the system of tonal music functions in such a way where they are a byproduct of the sequence of key signatures, and they are utilized and in certain occasions and therefore they exist.
I don't play many pieces written in C# major, it's usually written in Db. but i definitely have played either. as well as the other enharmonic keys.
I studied under some really fantastic musicians who were certain the keys "feel" different. I don't disagree with them. A string quartet (non-tempered instruments) playing in the flat vs sharp spelling of a given key will have a different flavor. it may be subtle, but it's there. And hey, the discussion here is "dopes it exist," not "the difference is so subtle i dont care."
btw, if you play in a rock band and rarely/never read music, i totally understand you personally having no reason to think outside of the 12/12 idea. that's sort of fine. but, since we're talking about it, again....
the answer is 15/15.