Multiply $4$ by $ \dfrac{y}{3} $ to get $ \dfrac{ 4y }{ 3 } $.

Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 4 \cdot \frac{y}{3} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{y}{3} \xlongequal{\text{Step 2}} \frac{ 4 \cdot y }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 4y }{ 3 } \end{aligned} $$

Subtract $y$ from $ \dfrac{4y}{3} $ to get $ \dfrac{ \color{purple}{ y } }{ 3 }$.

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

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{3}$.

$$ \begin{aligned} \frac{4y}{3} -y & \xlongequal{\text{Step 1}} \frac{4y}{3} - \frac{y}{\color{red}{1}} = \frac{ 4y }{ 3 } - \frac{ y \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4y } }{ 3 } - \frac{ \color{purple}{ 3y } }{ 3 }=\frac{ \color{purple}{ y } }{ 3 } \end{aligned} $$

Add $ \dfrac{y}{3} $ and $ \dfrac{2}{3} $ to get $ \dfrac{ y + 2 }{ \color{blue}{ 3 }}$.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{y}{3} + \frac{2}{3} & = \frac{y}{\color{blue}{3}} + \frac{2}{\color{blue}{3}} =\frac{ y + 2 }{ \color{blue}{ 3 }} \end{aligned} $$