Verified answer

4^(x + 2) = 8^(x – 1)

2^2(x + 2) = 2^3(x - 1)

2(x + 2) = 3(x - 1)

2x + 4 = 3x - 3

2x - 3x = - 3 - 4

- x = - 7

x = 7 answer//

I'd break down 4 and 8 to be powers of 2

4=2^2 8=2^3

2^2(x+2) = 2^3(x-1)

Now, you can just forget about the 2^

So,

2(x+2)=3(x-1)

Distribute & Solve

2x+4=3x-3

-2x -2x

4=x-3

+3 +3

7 = x

So, x=7