To solve this system of equations, we can use the method of substitution.
First, we can rearrange the second equation to solve for y:
-6x + y = 32
y = 6x + 32
Next, we can substitute this expression for y into the first equation:
4x - 8y = -36
4x - 8(6x + 32) = -36
Simplifying this equation, we get:
4x - 48x - 256 = -36
-44x = 220
x = -5
Now that we know the value of x, we can substitute it back into either of the original equations to solve for y. Using the second equation:
-6x + y = 32
-6(-5) + y = 32
y = 2
Therefore, the solution to the system of equations is:
x = -5
y = 2