1. **State the problem:** Simplify the expression $6(x-2)-4(x-8)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$6(x-2) = 6 \times x - 6 \times 2 = 6x - 12$$ $$-4(x-8) = -4 \times x + 4 \times 8 = -4x + 32$$ 3. **Rewrite the expression:** $$6x - 12 - 4x + 32$$ 4. **Combine like terms:** Combine the $x$ terms and the constant terms separately. $$6x - 4x = \cancel{6x} - \cancel{4x} = 2x$$ $$-12 + 32 = 20$$ 5. **Final simplified expression:** $$2x + 20$$ This is the simplified form of the original expression.