1. **State the problem:** Simplify the expression $$(3 + 6n^5 - 8n^4) - (-6n^4 - 3n + 8n^5).$$ 2. **Recall the rule:** When subtracting a polynomial, distribute the minus sign to each term inside the parentheses. 3. **Apply the subtraction:** $$3 + 6n^5 - 8n^4 + 6n^4 + 3n - 8n^5$$ 4. **Group like terms:** $$(6n^5 - 8n^5) + (-8n^4 + 6n^4) + 3 + 3n$$ 5. **Simplify each group:** $$(-2n^5) + (-2n^4) + 3 + 3n$$ 6. **Write the final simplified expression:** $$-2n^5 - 2n^4 + 3n + 3$$ This is the simplified form of the given expression.