\begin{tabular}{|l|}\hline Listen \\ What is the \( y \)-coordinate for the solution to the system of equations? \\ \( \left\{\begin{array}{l}8 x-4 y=-32 \\ 2 x+2 y=4\end{array}\right. \) \\ Enter your answer as the correct value, like this: 42 \\ If your answer is a fraction, enter it in simplest form, formatted like this: \( 3 / 14 \)\end{tabular}

To find the \( y \)-coordinate for the solution to the system of equations, we can solve the equations simultaneously. First, let's rewrite the second equation: \[ 2x + 2y = 4 \implies y = 2 - x. \] Now we can substitute \( y \) in the first equation: \[ 8x - 4(2 - x) = -32. \] Expanding this, we get: \[ 8x - 8 + 4x = -32 \implies 12x - 8 = -32 \implies 12x = -24 \implies x = -2. \] Now substituting \( x \) back into the equation for \( y \): \[ y = 2 - (-2) = 2 + 2 = 4. \] So, the \( y \)-coordinate for the solution to the system of equations is \( \boxed{4} \).