Add $ \dfrac{2}{3x^2+12x} $ and $ \dfrac{8}{2x} $ to get $ \dfrac{ \color{purple}{ 24x^2+100x } }{ 6x^3+24x^2 }$.

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}{ 2x }$ and the second by $\color{blue}{ 3x^2+12x }$.

$$ \begin{aligned} \frac{2}{3x^2+12x} + \frac{8}{2x} & = \frac{ 2 \cdot \color{blue}{ 2x }}{ \left( 3x^2+12x \right) \cdot \color{blue}{ 2x }} + \frac{ 8 \cdot \color{blue}{ \left( 3x^2+12x \right) }}{ 2x \cdot \color{blue}{ \left( 3x^2+12x \right) }} = \\[1ex] &=\frac{ \color{purple}{ 4x } }{ 6x^3+24x^2 } + \frac{ \color{purple}{ 24x^2+96x } }{ 6x^3+24x^2 }=\frac{ \color{purple}{ 24x^2+100x } }{ 6x^3+24x^2 } \end{aligned} $$