To evaluate the expression \( x - \frac{y}{3} \) when \( x = 9 \) and \( y = 6 \), we first substitute the values of \( x \) and \( y \) into the expression.
- Substitute \( x = 9 \) and \( y = 6 \):
\[ 9 - \frac{6}{3} \]
- Calculate \( \frac{6}{3} \):
\[ \frac{6}{3} = 2 \]
- Now replace \( \frac{6}{3} \) in the expression:
\[ 9 - 2 \]
- Finally, perform the subtraction:
\[ 9 - 2 = 7 \]
Thus, the value of the expression \( x - \frac{y}{3} \) when \( x = 9 \) and \( y = 6 \) is \( \boxed{7} \).