Solve the system of linear equations: $\begin{aligned} 3 x-6 y & =-39 \\ -4 x+8 y & =52\end{aligned}$

Step 1 ：\(1^{st}\) equation \(3x - 6y = -39\)

Step 2 ：\(2^{nd}\) equation \(-4x + 8y = 52\)

Step 3 ：Add \(1^{st}\) and \(2^{nd}\) equation: \((3x - 6y) + (-4x + 8y) = -39 + 52\)

Step 4 ：Solve for \(x\): \(x = 13\)

Step 5 ：Substitute \(x\) into the \(1^{st}\) equation: \(3(13) - 6y = -39\)

Step 6 ：Solve for \(y\): \(y = 2\)

Step 7 ：\(\boxed{\text{Solution: }(13, 2)}\)