When we open 1 side of the equation (x-4)^3 we get :
x^3 - 12x^2 + 48x - 64 =8
Now we simply
x^3 - 12x^2 + 48x = 72
Now we move everything to 1 side to isolate then set = 0 , then factor
If we are only looking for real answers, we could directly take the cube root and see that \(x=6\) is a solution. However, if we also want complex solutions we would proceed as @breadstick presented, and since we know \(x-6\) is a factor we could divide and use the quadratic formula from there.