1. **State the problem:** Simplify the expression $4(3+2x) - 2(3x-6) + 15x$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$4(3+2x) = 4 \times 3 + 4 \times 2x = 12 + 8x$$ $$-2(3x-6) = -2 \times 3x + (-2) \times (-6) = -6x + 12$$ 3. **Rewrite the expression with distributed terms:** $$12 + 8x - 6x + 12 + 15x$$ 4. **Combine like terms:** - Combine constants: $12 + 12 = 24$ - Combine $x$ terms: $8x - 6x + 15x = (8 - 6 + 15)x = 17x$ 5. **Final simplified expression:** $$24 + 17x$$ This is the simplified form of the original expression.