Note that (1/8)^(-1) = 8
So
(x - 4)^3 = 8 take the cube root of each side
x - 4 = (8)^(1/3)
x - 4 = 2 add 4 to both sides
x = 6
First figure out the right hand side.
1/8 to the power of -1 is the same thing as 8. Now, (x-4)^3 = 8
After this, get the cube root to the other side(you know what I mean) to get x-4 = 2.
Add 4 to both sides to get x = 6.
X is 6.
~~Hypotenuisance