To solve the equation \( 2x + 9 - 4x = x - 12 \), we can start by simplifying both sides of the equation.
First, combine like terms on the left side:
\[ 2x - 4x + 9 = x - 12 \]
This simplifies to:
\[ -2x + 9 = x - 12 \]
Next, we can move \( x \) from the right side to the left side by subtracting \( x \) from both sides:
\[ -2x - x + 9 = -12 \]
This gives us:
\[ -3x + 9 = -12 \]
Now, subtract 9 from both sides:
\[ -3x = -12 - 9 \]
Which simplifies to:
\[ -3x = -21 \]
Next, divide both sides by \(-3\):
\[ x = \frac{-21}{-3} = 7 \]
Thus, the value of \( x \) that makes the equation true is:
\[ \boxed{7} \]