Identify the equations of the asymptotes.

Step 1: Identify the equations of the asymptotes.
The given function is $f(x) = \frac{p}{x-2} + 4$.
For a hyperbola in the form $y = \frac{k}{x-a} + b$, the vertical asymptote is $x=a$ and the horizontal asymptote is $y=b$.
Comparing $f(x)$ to the general form, we have $a=2$ and $b=4$.
The equations of the asymptotes are $x=2$ and $y=4$.

The equations of the asymptotes are $x=2$ and $y=4$.

• Vertical asymptote: $\boxed{x=2}$
• Horizontal asymptote: $\boxed{y=4}$