1. **State the problem:** Simplify the expression $$(3x^2 + 3x - 3) - (6x^2 - 4x - 2)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to each term in the second group: $$3x^2 + 3x - 3 - 6x^2 + 4x + 2$$ 3. **Group like terms:** Combine terms with the same powers of $x$: $$ (3x^2 - 6x^2) + (3x + 4x) + (-3 + 2) $$ 4. **Simplify each group:** $$ 3x^2 - 6x^2 = \cancel{3x^2} - 6x^2 = -3x^2 $$ $$ 3x + 4x = 7x $$ $$ -3 + 2 = -1 $$ 5. **Write the simplified expression:** $$ -3x^2 + 7x - 1 $$ **Final answer:** $$\boxed{-3x^2 + 7x - 1}$$