1. **State the problem:** Simplify the expression $2(5a+8a)-3(4a-8)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$2(5a+8a) = 2 \times 5a + 2 \times 8a = 10a + 16a$$ $$-3(4a-8) = -3 \times 4a + (-3) \times (-8) = -12a + 24$$ 3. **Combine like terms:** Add the terms with $a$ and the constants separately. $$10a + 16a - 12a + 24 = (10a + 16a - 12a) + 24$$ 4. **Simplify the coefficients:** $$10a + 16a - 12a = (10 + 16 - 12)a = 14a$$ 5. **Write the final simplified expression:** $$14a + 24$$ **Answer:** The simplified form of the expression is $14a + 24$.