1. **State the problem:** Simplify the expression $$4(m+2n)+9(3m+6n)-12(5m+10n)$$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$4(m+2n) = 4m + 8n$$ $$9(3m+6n) = 27m + 54n$$ $$-12(5m+10n) = -60m - 120n$$ 3. **Rewrite the expression with distributed terms:** $$4m + 8n + 27m + 54n - 60m - 120n$$ 4. **Combine like terms:** Group the $m$ terms and the $n$ terms. $$ (4m + 27m - 60m) + (8n + 54n - 120n) $$ 5. **Simplify each group:** $$ (4 + 27 - 60)m + (8 + 54 - 120)n $$ $$ = (-29)m + (-58)n $$ $$ = -29m - 58n $$ **Final answer:** $$\boxed{-29m - 58n}$$