To subtract the expression \((h + 4)\) from \((4h + 9)\), you should distribute the negative sign across the terms in the second parentheses:
\[ (4h + 9) - (h + 4) = 4h + 9 - h - 4 \]
Now, combine like terms:
- Combine the \(h\) terms: \(4h - h = 3h\)
- Combine the constant terms: \(9 - 4 = 5\)
Putting it all together, you get:
\[ 3h + 5 \]
So, the result of the subtraction is:
\[ \boxed{3h + 5} \]