Let's solve each equation step by step.

1) -(3x-4) = 3x - 8
Distribute the negative sign:
-1 3x = -3x
-1 -4 = 4
Therefore, the equation becomes:
-3x + 4 = 3x - 8
Move 3x to the left side:
-3x - 3x + 4 = -8
-6x + 4 = -8
Subtract 4 from both sides:
-6x = -12
Divide by -6:
x = 2

2) 86(z-1) = 183
Distribute 86:
86z - 86 = 183
Add 86 to both sides:
86z = 269
Divide by 86:
z = 269/86
z ≈ 3.13

3) 2(x+6) = 2(x-3)
Distribute 2:
2x + 12 = 2x - 6
Subtract 2x from both sides:
12 = -6
This equation has no solution.

Therefore, x = 2, z ≈ 3.13, and there is no solution for the third equation.