The line $\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-4}{0}$ is 

The directrion ratios of any line parallel to $X$ axis are proprotional to  $k,0,0$

hence the given line $\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-4}{0}$ is not parallel to X- axis

similiarly this is not parallel to Y or Z axis

Equation of any plane parallel to XY planeis $z=k$

The given line lies on the plane $z=4$

Therefore, the line $\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-4}{0}$ lies on the plane parallel to Z axis