To evaluate the expression for \( d = 3 \), we will substitute \( d \) with \( 3 \) in the expression \(\frac{d - 9}{d - 6}\).
Starting with the substitution:
\[ \frac{3 - 9}{3 - 6} \]
Now, simplify the numerator and the denominator:
\[ 3 - 9 = -6 \] \[ 3 - 6 = -3 \]
Now, substituting these values back into the expression gives:
\[ \frac{-6}{-3} \]
Now simplify the fraction:
\[ \frac{-6}{-3} = 2 \]
Thus, the simplified answer is:
\[ \boxed{2} \]