1. **State the problem:** Simplify the expression $$(4n - 3n^3) - (3n^3 + 4n)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to the second group: $$4n - 3n^3 - 3n^3 - 4n$$ 3. **Combine like terms:** Group the terms with $n$ and the terms with $n^3$: $$(4n - 4n) + (-3n^3 - 3n^3)$$ 4. **Simplify each group:** $$0 + (-6n^3) = -6n^3$$ 5. **Final answer:** The simplified expression is $$-6n^3$$. This means the original expression simplifies to just $-6n^3$ after combining like terms.