Point $E$ is the centroid of face $ABC$ $($ which is a triangle$)$

Centroid $=\left[\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3}\right]$

$E=\left[\frac{2+(-3)+(-1)}{3},\frac{3+3+4}{3},\frac{-4+(-2)+2}{3}\right]$

$E=\left[\frac{-2}{3},\frac{10}{3},\frac{-4}{3}\right]$

Point $F$ is the centroid of face $ACD$

$F=\left[\frac{2+(-1)+3}{3},\frac{3+4+5}{3},\frac{-4+2+1}{3}\right]$

$F=\left[\frac{4}{3},\frac{12}{3},\frac{-1}{3}\right]=\left[\frac{4}{3},4,\frac{-1}{3}\right]$

Point $G$ is the centroid of face $ABD$

$G=\left[\frac{2+(-3)+3}{3},\frac{3+3+5}{3},\frac{-4+(-2)+1}{3}\right]$

$G=\left[\frac{2}{3},\frac{11}{3},\frac{-5}{3}\right]$

Now $EFG$ form a triangle, therefore centroid of $∆EFG$

$\Rightarrow \left[\frac{{\displaystyle \frac{-2}{3}}+{\displaystyle \frac{4}{3}}+{\displaystyle \frac{2}{3}}}{3},\frac{{\displaystyle \frac{10}{3}}+4+{\displaystyle \frac{11}{3}}}{3},\frac{{\displaystyle \frac{-4}{3}}+\left({\displaystyle \frac{-1}{3}}\right)+\left({\displaystyle \frac{-5}{3}}\right)}{3}\right]$

$\Rightarrow \left[\frac{4}{9},\frac{33}{9},\frac{-10}{9}\right]$

$\Rightarrow \left[\frac{4}{9},\frac{11}{3},\frac{-10}{9}\right]$