$\begin{array}{l}\frac{1}{2} x-\frac{2}{3} y=6 \\ \frac{1}{4} x+\frac{1}{3} y=-1\end{array}$

Step 1 ：\(\frac{1}{2}x - \frac{2}{3}y = 6\) and \(\frac{1}{4}x + \frac{1}{3}y = -1\)

Step 2 ：Multiply the second equation by 2 to make the coefficients of x the same: \(\frac{1}{2}x + \frac{2}{3}y = -2\)

Step 3 ：Add the two equations: \(\frac{1}{2}x - \frac{2}{3}y + \frac{1}{2}x + \frac{2}{3}y = 6 - 2\)

Step 4 ：Simplify: \(x = 4\)

Step 5 ：Substitute x back into the first equation: \(\frac{1}{2}(4) - \frac{2}{3}y = 6\)

Step 6 ：Simplify: \(2 - \frac{2}{3}y = 6\)

Step 7 ：Subtract 2 from both sides: \(-\frac{2}{3}y = 4\)

Step 8 ：Multiply both sides by \(-\frac{3}{2}\): \(y = -6\)

Step 9 ：\(\boxed{x = 4, y = -6}\)