To expand \( \frac{1}{3}(q - 6) \) using the Distributive Property, you multiply \( \frac{1}{3} \) by both terms inside the parentheses:
\[ \frac{1}{3}(q) - \frac{1}{3}(6) \]
This gives:
\[ \frac{1}{3}q - 2 \]
Thus, the correct answer is:
\[ \frac{1}{3}q - 2 \]