The essential formula here is to remember that for any a, b, and c, (ab)c=ab*c. So, for example, (23)4=23*4=212.
This problem then wants us to realize that 4=22 and 8=23. (In all these sorts of power problems, a good tip is to try to make all the power bases equal.) We then get (22)2x=(23)(3x-4), which by our formula leads to 2(2*2x))=2(3*(3x–4)). Now, if 2 to the power of two things is equal, those two things must be equal, so we can conclude 2*2x=3*(3x–4). The rest is algebra that I'm sure you know:
Hope that helps!