$\begin{array}{c}2 y+6=6 x \\ x=-x+3\end{array}$

Step 1 ：\(\begin{array}{c}2 y+6=6 x \\ x=-x+3\end{array}\)

Step 2 ：Solve the second equation for x: \(x = 3 - x\)

Step 3 ：Add x to both sides: \(2x = 3\)

Step 4 ：Divide both sides by 2: \(x = \frac{3}{2}\)

Step 5 ：Substitute the expression for x into the first equation: \(2y + 6 = 6\left(\frac{3}{2}\right)\)

Step 6 ：Simplify the equation: \(2y + 6 = 9\)

Step 7 ：Subtract 6 from both sides: \(2y = 3\)

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

Step 9 ：\(\boxed{x = \frac{3}{2}, y = \frac{3}{2}}\)