Multiply $ \dfrac{2a+4b}{6} $ by $ a $ to get $ \dfrac{ 2a^2+4ab }{ 6 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2a+4b}{6} \cdot a & \xlongequal{\text{Step 1}} \frac{2a+4b}{6} \cdot \frac{a}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 2a+4b \right) \cdot a }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2a^2+4ab }{ 6 } \end{aligned} $$

Add $ \dfrac{2a^2+4ab}{6} $ and $ 8b $ to get $ \dfrac{ \color{purple}{ 2a^2+4ab+48b } }{ 6 }$.

Step 1: Write $ 8b $ 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 $\color{blue}{6}$.

$$ \begin{aligned} \frac{2a^2+4ab}{6} +8b & \xlongequal{\text{Step 1}} \frac{2a^2+4ab}{6} + \frac{8b}{\color{red}{1}} = \frac{ 2a^2+4ab }{ 6 } + \frac{ 8b \cdot \color{blue}{ 6 }}{ 1 \cdot \color{blue}{ 6 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2a^2+4ab } }{ 6 } + \frac{ \color{purple}{ 48b } }{ 6 }=\frac{ \color{purple}{ 2a^2+4ab+48b } }{ 6 } \end{aligned} $$