subtracting oolynomials \[ (4 h+4)-(5 h+3) \]

Step 1 ：Given the polynomials \(4h + 4\) and \(5h + 3\)

Step 2 ：We are asked to subtract the second polynomial from the first. This involves subtracting like terms.

Step 3 ：Subtract the terms with the variable 'h': \(4h - 5h = -h\)

Step 4 ：Subtract the constant terms: \(4 - 3 = 1\)

Step 5 ：Combine these results to get the final polynomial: \(-h + 1\)

Step 6 ：Final Answer: \(\boxed{-h + 1}\)