Multiply the expressions and simplify. 
$\frac{3x+6}{y}\cdot \frac{xy+2y}{3}$

• A. $x-2$
• B. $x+2$
• C. ${(x+2)}^2$
• D. ${(x-2)}^2$

Answer: (C)

Verified step by step guidance

1. Start with the given expression: \(\frac{3x+6}{y} \cdot \frac{xy+2y}{3}\).
2. Factor where possible: notice that \$3x + 6\( can be factored as \)3(x + 2)\(, and \)xy + 2y\( can be factored as \)y(x + 2)$.
3. Rewrite the expression using these factorizations: \(\frac{3(x+2)}{y} \cdot \frac{y(x+2)}{3}\).
4. Multiply the numerators together and the denominators together: numerator is \(3(x+2) \cdot y(x+2)\) and denominator is \(y \cdot 3\).
5. Simplify by canceling common factors in numerator and denominator, such as \$3\( and \)y$, then combine the remaining factors to express the product in simplest form.