Let the points be $A(4,7,8), B(2,3,4),C(-1,-2,1)$ and $D(1,2,5)$

The direction rations of the line joining $A$ and $B$ is $(2-4),(3,-7),(4-8)$

On simplifying we get,

$(-2,-4,-4)$ (let this be $(a_1,b_1,c_1))$

The direction ratios of the line joining C and D is

$(1-(-1)),(2-(-2)),(5,-1)$

On simplifying we get,

$(2,4,4)$ (let this be $(a_2,b_2,c_2))$

For the line to be parallel,

$ \large \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Now substituting for $a_1,b_1,c_1$ and $a_2,b_2,c_2$ we get

$\large\frac{-2}{2}=\frac{-4}{4}=\frac{-4}{4}=1$

Since the ratios are equal, the lines are parallel.