1. **State the problem:** Simplify the expression $$\frac{2y - 2x \times \frac{2x}{y}}{y}$$. 2. **Recall the order of operations:** Multiplication and division are performed before addition and subtraction. 3. **Rewrite the expression clearly:** $$\frac{2y - 2x \cdot \frac{2x}{y}}{y}$$. 4. **Multiply inside the numerator:** Multiply $2x$ by $\frac{2x}{y}$: $$2x \times \frac{2x}{y} = \frac{4x^2}{y}$$. 5. **Substitute back into numerator:** $$2y - \frac{4x^2}{y}$$. 6. **Find common denominator in numerator:** To combine terms, write $2y$ as $\frac{2y^2}{y}$: $$\frac{2y^2}{y} - \frac{4x^2}{y} = \frac{2y^2 - 4x^2}{y}$$. 7. **Rewrite the entire expression:** $$\frac{\frac{2y^2 - 4x^2}{y}}{y} = \frac{2y^2 - 4x^2}{y \cdot y} = \frac{2y^2 - 4x^2}{y^2}$$. 8. **Factor numerator:** $$2y^2 - 4x^2 = 2(y^2 - 2x^2)$$. 9. **Final simplified expression:** $$\frac{2(y^2 - 2x^2)}{y^2}$$. This is the simplified form of the original expression.