1. **State the problem:** Simplify 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. **Calculate inside the first parentheses:** $$4^2 = 16$$ $$8 \cdot 2 = 16$$ So, $$4^2 + 8\cdot 2 = 16 + 16 = 32$$ 4. **Multiply inside the bracket:** $$-2 \times 32 = -64$$ 5. **Multiply by -9:** $$-9[-64] = -9 \times -64 = 576$$ 6. **Calculate inside the second bracket:** $$3 + 4 = 7$$ $$6^2 = 36$$ So, $$7 - 36 = -29$$ 7. **Multiply by 2:** $$2 \times (-29) = -58$$ 8. **Combine all parts:** $$-8 + 576 - 58$$ 9. **Simplify:** $$-8 + 576 = 568$$ $$568 - 58 = 510$$ **Final answer:** $$\boxed{510}$$