1. **State the problem:** Simplify the expression $-2x \cdot 2y - xy \cdot (-2x)$. 2. **Recall the rules:** Multiplication is distributive and associative. Also, multiplying two negatives gives a positive. 3. **Multiply the first term:** $-2x \cdot 2y = -4xy$. 4. **Multiply the second term:** $xy \cdot (-2x) = -2x^2y$. Since there is a minus sign before the term, it becomes $-(-2x^2y) = +2x^2y$. 5. **Rewrite the expression:** $-4xy + 2x^2y$. 6. **Factor common terms if possible:** Both terms have $xy$, so factor it out: $$-4xy + 2x^2y = yx(-4 + 2x)$$ 7. **Final simplified expression:** $$yx(-4 + 2x)$$ or equivalently $$xy(2x - 4)$$.