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 with distributed terms:** $$6a + 8b - 8a + b$$ 4. **Combine like terms:** For the terms with $a$: $$6a - 8a = \cancel{6a} - \cancel{8a} = -2a$$ For the terms with $b$: $$8b + b = 8b + 1b = 9b$$ 5. **Final simplified expression:** $$-2a + 9b$$ This is the simplified form of the given expression.