To subtract the expression \((3h + 4)\) from \((8h - 9)\), follow these steps:
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Distribute the negative sign across the second expression: \[ (8h - 9) - (3h + 4) = (8h - 9) - 3h - 4 \]
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Combine like terms:
- For the \(h\) terms: \(8h - 3h = 5h\)
- For the constant terms: \(-9 - 4 = -13\)
Putting it all together, you get: \[ 5h - 13 \]
Thus, the result is: \[ \boxed{5h - 13} \]