To solve the system of equations:
- \( 4x - 8y = -36 \)
- \( -6x + y = 32 \)
We can use substitution or elimination. Let's use the substitution method. First, we can solve the second equation for \( y \):
\[ y = 6x + 32 \]
Now, we can substitute this expression for \( y \) into the first equation:
\[ 4x - 8(6x + 32) = -36 \]
Expanding that:
\[ 4x - 48x - 256 = -36 \]
Combining like terms:
\[ -44x - 256 = -36 \]
Now, add 256 to both sides:
\[ -44x = 256 - 36 \] \[ -44x = 220 \]
Dividing both sides by -44 gives:
\[ x = \frac{220}{-44} = -5 \]
Now that we have \( x \), we can substitute it back into the equation for \( y \):
\[ y = 6(-5) + 32 \] \[ y = -30 + 32 \] \[ y = 2 \]
So the solution to the system of equations is:
\[ (x, y) = (-5, 2) \]
Thus, the final answer is:
\[ \boxed{(-5, 2)} \]