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