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 and Division, Addition and Subtraction). 3. **Evaluate inside the parentheses and exponents:** - Calculate $4^2 = 16$. - Calculate $8 \cdot 2 = 16$. - Calculate $6^2 = 36$. 4. **Simplify inside the brackets:** - Inside the first bracket: $4^2 + 8\cdot 2 = 16 + 16 = 32$. - Inside the second bracket: $(3+4) - 6^2 = 7 - 36 = -29$. 5. **Substitute back:** $$-8 - 9[-2(32)] + 2[-29]$$ 6. **Multiply inside the brackets:** $$-2(32) = -64$$ 7. **Substitute:** $$-8 - 9[-64] + 2[-29]$$ 8. **Multiply:** $$-9[-64] = 576$$ $$2[-29] = -58$$ 9. **Substitute:** $$-8 + 576 - 58$$ 10. **Perform addition and subtraction:** $$(-8 + 576) - 58 = 568 - 58 = 510$$ **Final answer:** $$510$$