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