Answer
$L_1$ and $L_3$ are parallel ; $L_2$ and $L_4$ are parallel.
Work Step by Step
From the given problem, we see that
$L_1$ has direction vector $\lt 6,-3,12\gt$
and $L_2$ has direction vector $\lt 2,1,4\gt $
$L_3$ has normal vector $\lt 1/2,-1/4,1\gt $
and
$L_4$ has normal vector $\lt 4,2,8\gt $ or $2\lt 2,1,4\gt $
Since, the direction vectors of $L_1$ and $L_3$ are constant multiples, they must be parallel .
Similarly, $L_2$ and $L_4$ are parallel.
