Multiply $2$ by $ \dfrac{a}{2a+6} $ to get $ \dfrac{ 2a }{ 2a+6 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $7$ by $ \dfrac{a}{a+3} $ to get $ \dfrac{ 7a }{ a+3 } $.

Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 7 \cdot \frac{a}{a+3} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{a}{a+3} \xlongequal{\text{Step 2}} \frac{ 7 \cdot a }{ 1 \cdot \left( a+3 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7a }{ a+3 } \end{aligned} $$

Add $ \dfrac{2a}{2a+6} $ and $ \dfrac{7a}{a+3} $ to get $ \dfrac{ \color{purple}{ 16a } }{ 2a+6 }$.

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

$$ \begin{aligned} \frac{2a}{2a+6} + \frac{7a}{a+3} & = \frac{ 2a }{ 2a+6 } + \frac{ 7a \cdot \color{blue}{ 2 }}{ \left( a+3 \right) \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 2a } }{ 2a+6 } + \frac{ \color{purple}{ 14a } }{ 2a+6 }=\frac{ \color{purple}{ 16a } }{ 2a+6 } \end{aligned} $$