1. **State the problem:** Expand and simplify the expression $-3(x - 2)^2$. 2. **Recall the formula:** The square of a binomial $(a - b)^2$ is expanded as $$ (a - b)^2 = a^2 - 2ab + b^2 $$ 3. **Apply the formula:** Here, $a = x$ and $b = 2$, so $$ (x - 2)^2 = x^2 - 2 \times x \times 2 + 2^2 = x^2 - 4x + 4 $$ 4. **Multiply by $-3$:** $$ -3(x^2 - 4x + 4) = -3x^2 + 12x - 12 $$ 5. **Final answer:** The expanded and simplified form is $$ \boxed{-3x^2 + 12x - 12} $$