3^(x-2) = 4^(2-x)

I know how to do these when the bottom numbers can be divided by each other to get the top equations down to solve, but how can I do this when when the numbers on the bottom are different?

I was thinking to times the 3 and 4 to get,

12^(4x-8) = 12^(6-3x)

and then I could do it from there. But am I even going about it the way I have to?

thanks