To solve for \( x \) in the equation
\[ \frac{12 - x}{9} = 11, \]
first, multiply both sides by 9 to eliminate the fraction:
\[ 12 - x = 11 \times 9. \]
Calculating the right side:
\[ 11 \times 9 = 99, \]
so the equation simplifies to:
\[ 12 - x = 99. \]
Next, subtract 12 from both sides:
\[ -x = 99 - 12, \]
which simplifies to:
\[ -x = 87. \]
Now, multiply both sides by -1 to solve for \( x \):
\[ x = -87. \]
Thus, the solution is
\[ \boxed{-87}. \]