1. **State the problem:** Simplify the expression $-4[8 \div 4 + 3(3 - 6)^2]$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). 3. **Evaluate inside the brackets:** - Calculate $8 \div 4$. - Calculate the expression inside the parentheses $(3 - 6)$. - Square the result of $(3 - 6)$. 4. **Calculate step-by-step:** - $8 \div 4 = 2$ - $3 - 6 = -3$ - $(-3)^2 = 9$ 5. **Substitute back:** - Expression inside brackets becomes $2 + 3 \times 9$ 6. **Multiply:** - $3 \times 9 = 27$ 7. **Add:** - $2 + 27 = 29$ 8. **Multiply by $-4$ outside the brackets:** - $-4 \times 29 = -116$ **Final answer:** $-116$