1. **State the problem:** Simplify the expression $-4(-3x - \frac{3}{3})$. 2. **Recall the distributive property:** $a(b + c) = ab + ac$. This means we multiply $-4$ by each term inside the parentheses. 3. **Simplify inside the parentheses:** $\frac{3}{3} = 1$, so the expression becomes $-4(-3x - 1)$. 4. **Distribute $-4$:** $$-4 \times (-3x) = 12x$$ $$-4 \times (-1) = 4$$ 5. **Combine the results:** $$12x + 4$$ **Final answer:** $12x + 4$