To solve the equation
\[ \frac{1}{3}(6x - 9) = -33, \]
first, multiply both sides by 3 to eliminate the fraction:
\[ 6x - 9 = -99. \]
Next, add 9 to both sides:
\[ 6x = -99 + 9, \]
which simplifies to
\[ 6x = -90. \]
Now, divide both sides by 6:
\[ x = \frac{-90}{6} = -15. \]
Thus, the solution for \( x \) is
\[ \boxed{-15}. \]