To solve the equation
\[ \frac{1}{3}(6x - 9) = -33, \]
we can start by eliminating the fraction. We can do this by multiplying both sides of the equation by 3:
\[ 6x - 9 = -33 \times 3. \]
Calculating the right side:
\[ -33 \times 3 = -99, \]
so we have:
\[ 6x - 9 = -99. \]
Next, we can add 9 to both sides to isolate the term with \(x\):
\[ 6x = -99 + 9. \]
Calculating the right side:
\[ -99 + 9 = -90, \]
so now we have:
\[ 6x = -90. \]
Next, divide both sides by 6 to solve for \(x\):
\[ x = \frac{-90}{6} = -15. \]
Therefore, the solution to the equation is:
\[ \boxed{-15}. \]
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