1. **State the problem:** Simplify the expression $$\frac{x - x - y + y}{2x^2 + 3xy + y^2} \cdot \frac{y^2 - 4x^2}{2x^2 + xy - y^2}$$. 2. **Simplify the numerator of the first fraction:** $$x - x - y + y = 0$$ because $x - x = 0$ and $-y + y = 0$. 3. Since the numerator of the first fraction is zero, the entire first fraction is zero regardless of the denominator (assuming denominator is not zero). 4. Therefore, the whole expression simplifies to: $$0 \cdot \frac{y^2 - 4x^2}{2x^2 + xy - y^2} = 0$$. 5. **Final answer:** $$0$$