To solve the system of equations using the substitution method, we first need to express one variable in terms of the other using one of the equations. Let's start with the second equation:
\[ y + 6 = 2x \]
We can isolate \(y\):
\[ y = 2x - 6 \]
Now that we have \(y\) in terms of \(x\), we can substitute this expression into the first equation. The first equation is:
\[ 9x - 3y = 12 \]
Substituting the expression for \(y\):
\[ 9x - 3(2x - 6) = 12 \]
Now, simplify the equation:
\[ 9x - 6x + 18 = 12 \]
Combine like terms:
\[ 3x + 18 = 12 \]
Next, isolate \(x\):
\[ 3x = 12 - 18 \]
\[ 3x = -6 \]
\[ x = -2 \]
Now that we have \(x\), we can find \(y\) by substituting \(x = -2\) back into the equation we found for \(y\):
\[ y = 2(-2) - 6 \]
\[ y = -4 - 6 \]
\[ y = -10 \]
So the solution to the system of equations is:
\[ (x, y) = (-2, -10) \]
Thus, the final answer is:
\[ (-2, -10) \]