1. **State the problem:** Simplify the expression $$\frac{2x + 4y}{9x - 18y} \times \frac{3x - 6y}{4x + 8y}$$. 2. **Identify common factors:** - In the numerator and denominator, look for common factors to factor out. 3. **Factor each term:** - $$2x + 4y = 2(x + 2y)$$ - $$9x - 18y = 9(x - 2y)$$ - $$3x - 6y = 3(x - 2y)$$ - $$4x + 8y = 4(x + 2y)$$ 4. **Rewrite the expression with factored terms:** $$\frac{2(x + 2y)}{9(x - 2y)} \times \frac{3(x - 2y)}{4(x + 2y)}$$ 5. **Cancel common factors:** - $$x + 2y$$ appears in numerator and denominator. - $$x - 2y$$ appears in numerator and denominator. 6. **Simplify the coefficients:** $$\frac{2}{9} \times \frac{3}{4} = \frac{2 \times 3}{9 \times 4} = \frac{6}{36} = \frac{1}{6}$$ 7. **Final simplified expression:** $$\frac{1}{6}$$ **Answer:** The simplified form of the expression is $$\frac{1}{6}$$.