Answer
$p= 2$
Work Step by Step
Given \begin{equation}
\sqrt{p+6}=\sqrt{3 p+2}.
\end{equation} Start by squaring both sides of the equation to eliminate the radical sign and solve for $p$.
\begin{equation}
\begin{aligned}
\sqrt{p+6}&=\sqrt{3 p+2} \\
\left( \sqrt{p+6}\right)^2&= \left(\sqrt{3 p+2}\right)^2\\
p+6& = 3 p+2\\
6-2& = 3p-p\\
4& =2p\\
2&= p.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\sqrt{2 +6}& \stackrel{?}{=} \sqrt{3 \cdot 2+2} \\
\sqrt{8}& =\sqrt{8}\checkmark.
\end{aligned}
\end{equation} The solution is $p= 2$.
