Mosiah mounts a modest expedition to discover what happened to the earlier people. That there are 16 people in the group tells us both that there was some potential danger imagined for the expedition, as well as that this was a search party, not a settlement. It was a group large enough for self-defense but small enough for rapid movement.
There is no clear reason for selecting 16 men for the expedition. Had the Zarahemlaites selected 12 men, we would immediately know that there was a symbolism that was attached to the number in addition the pragmatics of size. Nevertheless, there is a possibility that gives us reason for 16 which comes from the Mesoamerican context. Just as the numbers 3,7,12, and 40 have special meaning in our received scriptures from the Old World, there as a Mesoamerican symbolism attached to numbers, particularly numbers involving the number 4. As four fours, 16 becomes a significant number in a Mesoamerican context.
The number four in Mesoamerica is symbolic of completion or wholeness. The number four figures prominently in many of the creation accounts, appearing as four world trees, four deities assigned to the four directions, and four ages of creation (the Mexica five age, or 5 "sun" system is probably a later elaboration of the more basic Mesoamerican 4 sun mythology. See Gardner, Brant. "The Aztec `Legend of the Suns': A Multi-Dimensional Approach to the Ethnohistory of Myth." In: Symbol and Meaning Beyond the Closed Community. Ed. Gary Gossen. Institute for Mesoamerican Studies, State University of New York, Albany. 1986, pp. 19-34). As four fours, a group of 16 would have a very satisfying "feel" to a native Mesoamerican.