Given: $P(3,2,-4),\:Q(5,4,-6)\:\:and\:\:R(9,8,-10)$ are collinear.

Let the ratio in which $Q$ divides $PR$ be $ k:1$

$\therefore$ We know from section formula that the coordinates of $Q$ is given by

$Q\big(\large\frac{9k+3}{k+1},\frac{8k+2}{k+1},\frac{-10k-4}{k+1}\big)$

But given that $Q(5,4,-6)$

$\Rightarrow\:5=\large\frac{9k+3}{k+1}$

$\Rightarrow\:5k+5=9k+3$

$\Rightarrow\:4k=2$ or $k=\large\frac{1}{2}$

$\therefore$ the required ratio is $\large\frac{1}{2}$$\::\:1=1:2$