1. **State the problem:** Evaluate the expression $$-8 - 9[-2(4^2 + 8 \cdot 2)] + 2[(3 + 4) - 6^2]$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). 3. **Evaluate inside the parentheses and exponents:** - Calculate $4^2 = 16$ - Calculate $8 \cdot 2 = 16$ - So, inside the first bracket: $4^2 + 8 \cdot 2 = 16 + 16 = 32$ - Calculate $6^2 = 36$ - Inside the second bracket: $(3 + 4) - 6^2 = 7 - 36 = -29$ 4. **Substitute back:** $$-8 - 9[-2(32)] + 2[-29]$$ 5. **Multiply inside the brackets:** $$-2(32) = -64$$ 6. **Substitute:** $$-8 - 9[-64] + 2[-29]$$ 7. **Multiply:** $$-9 \times -64 = 576$$ $$2 \times -29 = -58$$ 8. **Substitute:** $$-8 + 576 - 58$$ 9. **Perform addition and subtraction from left to right:** $$(-8 + 576) - 58 = 568 - 58 = 510$$ **Final answer:** $$510$$