Multiply $8c$ by $ \dfrac{d}{3} $ to get $ \dfrac{ 8cd }{ 3 } $.

Step 1: Write $ 8c $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 8c \cdot \frac{d}{3} & \xlongequal{\text{Step 1}} \frac{8c}{\color{red}{1}} \cdot \frac{d}{3} \xlongequal{\text{Step 2}} \frac{ 8c \cdot d }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8cd }{ 3 } \end{aligned} $$

Add $ \dfrac{8cd}{3} $ and $ 10 $ to get $ \dfrac{ \color{purple}{ 8cd+30 } }{ 3 }$.

Step 1: Write $ 10 $ 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 second fraction by $\color{blue}{3}$.

$$ \begin{aligned} \frac{8cd}{3} +10 & \xlongequal{\text{Step 1}} \frac{8cd}{3} + \frac{10}{\color{red}{1}} = \frac{ 8cd }{ 3 } + \frac{ 10 \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 8cd } }{ 3 } + \frac{ \color{purple}{ 30 } }{ 3 }=\frac{ \color{purple}{ 8cd+30 } }{ 3 } \end{aligned} $$