Multiply $6$ by $ \dfrac{x}{3} $ to get $ \dfrac{ 6x }{ 3 } $.

Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 6 \cdot \frac{x}{3} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{x}{3} \xlongequal{\text{Step 2}} \frac{ 6 \cdot x }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 6x }{ 3 } \end{aligned} $$

Add $ \dfrac{5}{x^2-4x-12} $ and $ \dfrac{6x}{3} $ to get $ \dfrac{ \color{purple}{ 6x^3-24x^2-72x+15 } }{ 3x^2-12x-36 }$.

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 $\color{blue}{ x^2-4x-12 }$.

$$ \begin{aligned} \frac{5}{x^2-4x-12} + \frac{6x}{3} & = \frac{ 5 \cdot \color{blue}{ 3 }}{ \left( x^2-4x-12 \right) \cdot \color{blue}{ 3 }} + \frac{ 6x \cdot \color{blue}{ \left( x^2-4x-12 \right) }}{ 3 \cdot \color{blue}{ \left( x^2-4x-12 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 15 } }{ 3x^2-12x-36 } + \frac{ \color{purple}{ 6x^3-24x^2-72x } }{ 3x^2-12x-36 } = \\[1ex] &=\frac{ \color{purple}{ 6x^3-24x^2-72x+15 } }{ 3x^2-12x-36 } \end{aligned} $$