Divide $ \dfrac{2}{p-2} $ by $ 6 $ to get $ \dfrac{ 2 }{ 6p-12 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{2}{p-2} }{6} & \xlongequal{\text{Step 1}} \frac{2}{p-2} \cdot \frac{\color{blue}{1}}{\color{blue}{6}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot 1 }{ \left( p-2 \right) \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2 }{ 6p-12 } \end{aligned} $$

Divide $ \dfrac{2}{6p-12} $ by $ p+2 $ to get $ \dfrac{2}{6p^2-24} $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{2}{6p-12} }{p+2} & \xlongequal{\text{Step 1}} \frac{2}{6p-12} \cdot \frac{\color{blue}{1}}{\color{blue}{p+2}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot 1 }{ \left( 6p-12 \right) \cdot \left( p+2 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2 }{ 6p^2+ \cancel{12p} -\cancel{12p}-24 } = \frac{2}{6p^2-24} \end{aligned} $$

Add $ \dfrac{2}{6p^2-24} $ and $ \dfrac{8}{p^2-4} $ to get $ \dfrac{ \color{purple}{ 50 } }{ 6p^2-24 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{6}$.

$$ \begin{aligned} \frac{2}{6p^2-24} + \frac{8}{p^2-4} & = \frac{ 2 }{ 6p^2-24 } + \frac{ 8 \cdot \color{blue}{ 6 }}{ \left( p^2-4 \right) \cdot \color{blue}{ 6 }} = \\[1ex] &=\frac{ \color{purple}{ 2 } }{ 6p^2-24 } + \frac{ \color{purple}{ 48 } }{ 6p^2-24 }=\frac{ \color{purple}{ 50 } }{ 6p^2-24 } \end{aligned} $$