1. **State the problem:** Simplify the expression $37(-10) - 4(2 \times 4) - 77$. 2. **Recall the order of operations:** Perform multiplication and division before addition and subtraction. 3. **Calculate each multiplication:** $$37 \times (-10) = -370$$ $$4 \times (2 \times 4) = 4 \times 8 = 32$$ 4. **Substitute back into the expression:** $$-370 - 32 - 77$$ 5. **Perform the subtraction step-by-step:** $$-370 - 32 = -402$$ $$-402 - 77 = -479$$ 6. **Final answer:** $$\boxed{-479}$$