1. **State the problem:** Simplify the expression $2(3a+4b)-(8a-b)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$2(3a+4b) = 2 \times 3a + 2 \times 4b = 6a + 8b$$ $$-(8a-b) = -1 \times 8a + (-1) \times (-b) = -8a + b$$ 3. **Rewrite the expression:** $$6a + 8b - 8a + b$$ 4. **Group like terms:** $$(6a - 8a) + (8b + b)$$ 5. **Simplify each group:** $$6a - 8a = \cancel{6a} - \cancel{8a} = -2a$$ $$8b + b = 8b + 1b = 9b$$ 6. **Final simplified expression:** $$-2a + 9b$$