To solve this equation, we need to follow the order of operations (PEMDAS/BODMAS):

First, let's simplify the expression inside the parentheses: (129 - x÷8)
129 - x÷8 = 129 - (x/8)

Next, divide x by 8:
129 - (x/8) = 129 - (1/8)x

Now, let's substitute this expression back into the original equation:
32 + (129 - (1/8)x) ÷ 4 = 64

Now, solve the expression inside the parentheses:
129 - (1/8)x = 129 - x/8

Next, multiply by 4 to get rid of the division:
4*(129 - x/8) = 516 - x/2

Now, substitute back into the equation:
32 + (516 - x/2) = 64

Next, simplify the expression inside the parentheses:
32 + 516 - x/2 = 64
548 - x/2 = 64

Now, subtract 548 from both sides of the equation:
-x/2 = -484

Finally, multiply both sides by 2 to isolate x:
x = 968

Therefore, the solution to the equation is x = 968.