Let $l, m, n$ be the direction cosines of the line of shortest distance. As it is perpendicular to given lines,

$3l - m + n = 0$

$-3l + 2m + 4n = 0$

$\implies \frac{l}{-6} = \frac{m}{-15} = \frac{n}{3} $

$\implies \frac{l}{-2} = \frac{m}{-5} = \frac{n}{1} $

$\implies$ distance $ = \left |\frac{(3- (-3)).(-2) + (8-(-7)).(-5) + (3-6).1}{\sqrt{{(-2)}^2 + {(-5)}^2 + 1^2}} \right | = \left |\frac{-90}{\sqrt{30}} \right | = 3\sqrt{30}$