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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $y+8$ from $ \dfrac{y^4z}{3} $ to get $ \dfrac{ \color{purple}{ y^4z-3y-24 } }{ 3 }$.

Step 1: Write $ y+8 $ 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 $\color{blue}{3}$.

$$ \begin{aligned} \frac{y^4z}{3} -y+8 & \xlongequal{\text{Step 1}} \frac{y^4z}{3} - \frac{y+8}{\color{red}{1}} = \frac{ y^4z }{ 3 } - \frac{ \left( y+8 \right) \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ y^4z } }{ 3 } - \frac{ \color{purple}{ 3y+24 } }{ 3 }=\frac{ \color{purple}{ y^4z - \left( 3y+24 \right) } }{ 3 } = \\[1ex] &=\frac{ \color{purple}{ y^4z-3y-24 } }{ 3 } \end{aligned} $$