$\begin{array}{r}4 x-2 y=-6 \\ x+4 y=-24\end{array}$

Step 1 ：Given the system of equations: \(4x - 2y = -6\) and \(x + 4y = -24\)

Step 2 ：First, we solve the first equation for x: \(x = \frac{y}{2} - \frac{3}{2}\)

Step 3 ：Next, we substitute x in the second equation: \(\frac{9y}{2} - \frac{3}{2} = -24\)

Step 4 ：Solving this equation gives us the value of y: \(y = -5\)

Step 5 ：Substituting y = -5 into the first equation, we find the value of x: \(x = -4\)

Step 6 ：Final Answer: The solution to the system of equations is \(\boxed{x = -4, y = -5}\)