Add $ \dfrac{3}{n+6} $ and $ \dfrac{7}{n-2} $ to get $ \dfrac{ \color{purple}{ 10n+36 } }{ n^2+4n-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}{ n-2 }$ and the second by $\color{blue}{ n+6 }$.

$$ \begin{aligned} \frac{3}{n+6} + \frac{7}{n-2} & = \frac{ 3 \cdot \color{blue}{ \left( n-2 \right) }}{ \left( n+6 \right) \cdot \color{blue}{ \left( n-2 \right) }} + \frac{ 7 \cdot \color{blue}{ \left( n+6 \right) }}{ \left( n-2 \right) \cdot \color{blue}{ \left( n+6 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 3n-6 } }{ n^2-2n+6n-12 } + \frac{ \color{purple}{ 7n+42 } }{ n^2-2n+6n-12 }=\frac{ \color{purple}{ 10n+36 } }{ n^2+4n-12 } \end{aligned} $$