x is a power.

Okay.

4^x = 8^(2-x)

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

2^(2*x) = 2^[3(2-x)]

2x = 3(2-x)

2x = 6 -3x

2x +3x = 6

5x = 6

x = 6/5 ---------answer.

Check,

4^x = 8^(2-x)

4^(6/5) =? 8^(2 -6/5)

4^(1.2) =? 8^(0.8)

Using a calculator,

5.278031643 =? 5.278031643

Yes, so, OK.