1. **State the problem:** Simplify the expression $$2(4x - 4) - 3(x - 3)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$2(4x - 4) = 2 \times 4x - 2 \times 4 = 8x - 8$$ $$-3(x - 3) = -3 \times x + (-3) \times (-3) = -3x + 9$$ 3. **Rewrite the expression:** $$8x - 8 - 3x + 9$$ 4. **Combine like terms:** Combine the $x$ terms: $$8x - 3x = 5x$$ Combine the constants: $$-8 + 9 = 1$$ 5. **Final simplified expression:** $$5x + 1$$ Therefore, the simplified expression is **5x + 1**.