Answer
$t=\dfrac{4r}{3p^2}$
Work Step by Step
Using the properties of equality to solve for $t,$ the given equation, $p=2\sqrt{\dfrac{r}{3t}},$ is equivalent to
\begin{align*}\require{cancel}
(p)^2&=\left(2\sqrt{\dfrac{r}{3t}}\right)^2
\\\\
p^2&=\left(2\right)^2\left(\sqrt{\dfrac{r}{3t}}\right)^2
\\\\
p^2&=4\left(\dfrac{r}{3t}\right)
\\\\
p^2&=\dfrac{4r}{3t}
\\\\
3t(p^2)&=\left(\dfrac{4r}{3t}\right)3t
\\\\
t(3p^2)&=4r
\\\\
\dfrac{t(\cancel{3p^2})}{\cancel{3p^2}}&=\dfrac{4r}{3p^2}
\\\\
t&=\dfrac{4r}{3p^2}
.\end{align*}
Hence, in terms of $t,$ the given equation is equivalen to $t=\dfrac{4r}{3p^2}$.
