In verse 9, Amulon recognized Alma as the former fellow priest of King Noah. The afflictions suffered by the people of Alma were so great that "they began to cry mightily to God" (24:10). The Lamanites took steps to prevent their public prayers, but the people continued to pray in their hearts. We can always do that! The Nephites approached this problem by three principles: turn to him, trust him, and serve him.
Three times the voice of the Lord came to Alma and his people. The Lord told them to be of good comfort and covenanted to deliver them out of bondage and to ease their burdens (24:13–14). When the burdens were borne with cheerfulness and patience, the voice of the Lord came again, saying, "Be of good comfort, for on the morrow I will deliver you out of bondage"; (24:16). And indeed, the people escaped in the night, with the help of the Lord, to a valley they called "the valley Alma," where they gave thanks, and then a third time, the Lord warned Alma to leave quickly for Zarahemla and told him that he would "stop the Lamanites in this valley" (24:23).
Twelve days later they arrived safely in Zarahemla and were received with joy (24:25). These durations of travel give readers a fairly clear idea of how far it was from the Land of Nephi to the Land of Zarahemla—only about 200 miles.
On the frequent use of the Exodus of the Israelites from Egypt as a type or pattern of the liberations of Limhi’s people from the Lamanites and of Alma’s people from Amulon, see S. Kent Brown. "The Exodus Pattern of the Book of Mormon," in From Jerusalem to Zarahemla: Literary and Historical Studies of the Book of Mormon (Provo, UT: Religious Studies Center, Brigham Young University, 1998), 75–98.
On distances in Book of Mormon geography, see John L. Sorenson, An Ancient American Setting for the Book of Mormon (Salt Lake City, UT: Deseret Book, 1985), 8–23.