Add $ \dfrac{p^2+8p+12}{p} $ and $ 6 $ to get $ \dfrac{ \color{purple}{ p^2+14p+12 } }{ p }$.

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

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

$$ \begin{aligned} \frac{p^2+8p+12}{p} +6 & \xlongequal{\text{Step 1}} \frac{p^2+8p+12}{p} + \frac{6}{\color{red}{1}} = \frac{ p^2+8p+12 }{ p } + \frac{ 6 \cdot \color{blue}{ p }}{ 1 \cdot \color{blue}{ p }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ p^2+8p+12 } }{ p } + \frac{ \color{purple}{ 6p } }{ p }=\frac{ \color{purple}{ p^2+14p+12 } }{ p } \end{aligned} $$