Here the given expression is $\left(x^2+\frac{1}{x}\right)^{2 n}$.
$$
\begin{aligned}
&T_{r+1}={ }^{2 n} C_r\left(x^2\right)^{2 n-r}\left(\frac{1}{x}\right)^r \\
&={ }^{2 n} C_r x^{4 n-2 r} x^{-r}={ }^{2 n} C_r x^{4 n-3 r}
\end{aligned}
$$
Let $4 n-3 r=p$
$$
\begin{aligned}
&{\left[\text { as } x^p \text { occurs in expansion of }\left(x^2+\frac{1}{x}\right)^{2 n}\right]} \\
&\Rightarrow 3 r=4 n-p \Rightarrow r=\frac{4 n-p}{3}
\end{aligned}
$$
$\therefore$ Coefficient of $x^p={ }^{2 n} C_r=\frac{(2 n) !}{r !(2 n-r) !}$


$$
\begin{aligned}
&=\frac{(2 n) !}{\left(\frac{4 n-p}{3}\right) !\left(2 n-\frac{4 n-p}{3}\right) !} \\
&=\frac{(2 n) !}{\left(\frac{4 n-p}{3}\right) !\left(\frac{6 n-4 n+p}{3}\right) !} \\
&=\frac{(2 n) !}{\left(\frac{4 n-p}{3}\right) !\left(\frac{2 n+p}{3}\right) !}
\end{aligned}
$$