Multiply $3$ by $ \dfrac{y}{6} $ to get $ \dfrac{ 3y }{ 6 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 3 \cdot \frac{y}{6} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{y}{6} \xlongequal{\text{Step 2}} \frac{ 3 \cdot y }{ 1 \cdot 6 } \xlongequal{\text{Step 3}} \frac{ 3y }{ 6 } \end{aligned} $$

Multiply $ \dfrac{3y}{6} $ by $ x $ to get $ \dfrac{ 3xy }{ 6 } $.

Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3y}{6} \cdot x & \xlongequal{\text{Step 1}} \frac{3y}{6} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3y \cdot x }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3xy }{ 6 } \end{aligned} $$

Multiply $ \dfrac{3xy}{6} $ by $ y $ to get $ \dfrac{ 3xy^2 }{ 6 } $.

Step 1: Write $ y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3xy}{6} \cdot y & \xlongequal{\text{Step 1}} \frac{3xy}{6} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3xy \cdot y }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3xy^2 }{ 6 } \end{aligned} $$

Add $2x$ and $ \dfrac{3xy^2}{6} $ to get $ \dfrac{ \color{purple}{ 3xy^2+12x } }{ 6 }$.

Step 1: Write $ 2x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 6 }$.

$$ \begin{aligned} 2x+ \frac{3xy^2}{6} & \xlongequal{\text{Step 1}} \frac{2x}{\color{red}{1}} + \frac{3xy^2}{6} = \frac{ 2x \cdot \color{blue}{ 6 }}{ 1 \cdot \color{blue}{ 6 }} + \frac{ 3xy^2 }{ 6 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 12x } }{ 6 } + \frac{ \color{purple}{ 3xy^2 } }{ 6 }=\frac{ \color{purple}{ 3xy^2+12x } }{ 6 } \end{aligned} $$