Go to galaxy map and click the clear route button. It will be in the same place the original route icon was when you created the route.
If you can't see your destination on the screen, type it into the blank box under the Navigation tab, then hit Enter - the map view will whizz along to your destination. To have the game calculate your waypoints, click on the star in the map, then select 'Plot Route'.
Currently, the galaxy map can only plot routes that do not exceed 1,000 ly (less if you're near the galactic core due to the sheer density of stars there), so if the destination you want to get to is further away than that, you need to plot it in segments.
The problem is most likely that his ship can't cover the jump distances required for one or more of the jumps in any possible route.