Zoram and his army effect a rout on the Lamanite army. Even thought he Lamanite army must have been sizeable to have wrecked such destruction on Ammonihah, they had been in battle, and on a forced march through difficult terrain thereafter. In comparison, Zoram's troops would have been much fresher, not having yet fought, and having come a lesser distance though presumably easier terrain. We might expect that there was a reasonably well traveled road between Zarahemla and Manti, and nothing that would prevent Zoram from using that method of moving his troops.
The only slight difficulty in this passage is the ambiguous "brought by their brethren to possess their own lands." It is not easy to determine to whom the "own lands" originally belonged. It could just as easily refer to the Ammonihahite prisoners as the Zarahemlaites. However, the subsequent verses make it clear that no one entered the former land of Ammonihah, so we are to understand that the released prisoners were given new lands from the land of Zarahemla.