1. **State the problem:** Simplify the expression $4x[-2x]$. 2. **Recall the rule:** Multiplying a number by a product inside brackets means multiplying the number by each term inside the brackets. 3. **Apply multiplication:** $$4x \times (-2x) = 4 \times (-2) \times x \times x$$ 4. **Multiply constants:** $$4 \times (-2) = -8$$ 5. **Multiply variables:** $$x \times x = x^2$$ 6. **Combine results:** $$-8x^2$$ **Final answer:** $-8x^2$