1. **State the problem:** Simplify the expression $6(2x-3)-2(2x+1)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$6(2x-3) = 6 \times 2x - 6 \times 3 = 12x - 18$$ $$-2(2x+1) = -2 \times 2x - 2 \times 1 = -4x - 2$$ 3. **Combine the results:** $$12x - 18 - 4x - 2$$ 4. **Group like terms:** $$ (12x - 4x) + (-18 - 2)$$ 5. **Simplify each group:** $$12x - 4x = 8x$$ $$-18 - 2 = -20$$ 6. **Write the final simplified expression:** $$8x - 20$$