To solve for \( q \) in the equation
\[ 2 = \frac{q}{3} - 2, \]
we can start by isolating \( \frac{q}{3} \). First, add 2 to both sides of the equation:
\[ 2 + 2 = \frac{q}{3}, \]
which simplifies to
\[ 4 = \frac{q}{3}. \]
Next, to solve for \( q \), multiply both sides by 3:
\[ q = 4 \times 3, \]
which gives us
\[ q = 12. \]
Thus, the solution is
\[ \boxed{12}. \]