To solve the equation, we will first simplify each side separately.

Simplify the left side of the equation:
-8 + 4(7 + 8x)
= -8 + 28 + 32x
= 20 + 32x

Simplify the right side of the equation:
4x - 6(1 - x + 4x)
= 4x - 6 + 6x - 24x
= 4x - 6 + 6x - 24x
= -18x - 6

Now, we have the equation: 20 + 32x = -18x - 6

To solve for x, we will isolate x on one side of the equation. Let's move all terms with x to the left side:

32x + 18x = -6 - 20
50x = -26

Now, divide by 50 on both sides:
x = -26/50
x = -13/25

Therefore, the solution to the equation is x = -13/25.