1. **State the problem:** Subtract the expression $ (7u + 4) $ from $ (-9u + 3) $, i.e., calculate $$ (-9u + 3) - (7u + 4) $$. 2. **Use the distributive property:** When subtracting, distribute the minus sign to each term inside the second parentheses: $$ (-9u + 3) - (7u + 4) = -9u + 3 - 7u - 4 $$ 3. **Combine like terms:** Group the $u$ terms and the constants: $$ (-9u - 7u) + (3 - 4) $$ 4. **Simplify:** $$ -16u - 1 $$ 5. **Compare with the given answer:** The user's answer is $-2u - 1$, which is incorrect. **Final answer:** $$\boxed{-16u - 1}$$