Add $ \dfrac{4}{2x+4} $ and $ \dfrac{5}{3x+6} $ to get $ \dfrac{ \color{purple}{ 22 } }{ 6x+12 }$.

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

$$ \begin{aligned} \frac{4}{2x+4} + \frac{5}{3x+6} & = \frac{ 4 \cdot \color{blue}{ 3 }}{ \left( 2x+4 \right) \cdot \color{blue}{ 3 }} + \frac{ 5 \cdot \color{blue}{ 2 }}{ \left( 3x+6 \right) \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 12 } }{ 6x+12 } + \frac{ \color{purple}{ 10 } }{ 6x+12 }=\frac{ \color{purple}{ 22 } }{ 6x+12 } \end{aligned} $$