To evaluate the expression \( \frac{h}{h + 9} \) for \( h = -12 \), we start by substituting \(-12\) for \(h\):
\[ \frac{-12}{-12 + 9} \]
Now, simplify the denominator:
\[ -12 + 9 = -3 \]
So the expression becomes:
\[ \frac{-12}{-3} \]
Now, divide \(-12\) by \(-3\):
\[ \frac{-12}{-3} = 4 \]
Thus, the simplified value of the expression when \( h = -12 \) is:
\[ \boxed{4} \]