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.