First ask yourself, is there ever a value for which 12^x is odd?

At first it feels like, no, there isn't. Because no matter how many times you multiply an even number by itself it'll always be even (remembering that negative exponents usually create fractions, which are neither odd nor even).

UNLESS you remember that "x" is an integer. And "0" is an integer.

So, is there an integer value for which 12^x is odd?

Yes, 12^0 = 1. And 1 is an odd number. So, x=0, and 0^12 = 0. 0 is your answer.

The other tricky thing to remember here is that if you get too excited and go "12^0=1", you might forget what you're solving for an go "oh! x=1!". NOPE. Remember the question that you're answering; it's right in front of you, so you can double check what the question is that you're answering and make sure you're answering it