1. **State the problem:** We need to solve the expression $4^2(-4-4)(-4+1)$. 2. **Recall the order of operations:** Calculate powers first, then evaluate expressions inside parentheses, and finally multiply. 3. **Calculate the power:** $$4^2 = 16$$ 4. **Evaluate the expressions inside parentheses:** $$-4 - 4 = -8$$ $$-4 + 1 = -3$$ 5. **Substitute these values back into the expression:** $$16 \times (-8) \times (-3)$$ 6. **Multiply step-by-step:** $$16 \times (-8) = -128$$ $$-128 \times (-3) = 384$$ 7. **Final answer:** $$384$$