Let the point R₁, trisects the line PQ i.e., it divides the line in the ratio 1:2

$\begin{array}{l}\Rightarrow {\mathrm{R}}_1=\left[\frac{1\times 10+2\times 4}{1+2},\frac{1\times (-16)+2\times 2}{1+2},\frac{1\times 6+2\times (-6)}{1+2}\right]\\ =\left(\frac{10+8}{3},\frac{-16+4}{3},\frac{6-12}{3}\right)=\left(\frac{18}{3},\frac{-12}{3},\frac{-6}{3}\right)\\ =(6,-4,-2)\end{array}$

Again, let the point R₂ divides PQ internally in the ratio 2: 1. Then, 

$\begin{array}{l}\Rightarrow R_2=\left[\frac{2\times 10+1\times 4}{2+1},\frac{2\times (-16)+1\times 2}{2+1},\frac{2\times 6+1\times (-6)}{1+2}\right]\\ =\left(\frac{20+4}{3},\frac{-32+2}{3},\frac{12-6}{3}\right)=\left(\frac{24}{3},\frac{-30}{3},\frac{6}{3}\right)\\ =(8,-10,2)\end{array}$

Hence, required points are (6,-4, - 2) and (8, - 10,2).