Alma 17:16 - 17:20
Alma 17:16 Therefore, this was the cause for which the sons of Mosiah had undertaken the work, that perhaps they might bring them unto repentance; that perhaps they might bring them to know of the plan of redemption.
The bottom line for why the sons of Mosiah went forth among the Lamanites was to get them to change their hearts and minds and come to repentance; to start living the gospel so they might take advantage of the plan of happiness.
Alma 17:17 Therefore they separated themselves one from another, and went forth among them, every man alone, according to the word and power of God which was given unto him.
These brethren divided themselves up into smaller groups and went in whatever direction as the Spirit directed them to go.
Alma 17:18 Now Ammon being the chief among them, or rather he did administer unto them, and he departed from them, after having blessed them according to their several stations, having imparted the word of God unto them, or administered unto them before his departure; and thus they took their several journeys throughout the land.
Before they split up, Ammon gave them their last instructions as head of the expedition. He blessed them to have whatever gifts they needed to accomplish their missions to whatever part of the land of Nephi they found themselves directed to go.
This was a very dangerous thing these boys were going to attempt. They could just easily be killed as not. I’m sure Ammon probably put his hands on each one of them to give them individual blessings. Couple this with the simple fact they were actual brothers and you can since the anxiety they all must have had for each other’s safety.
Alma 17:19 And Ammon went to the land of Ishmael, the land being called after the sons of Ishmael, who also became Lamanites.
Ammon headed for the land of Ishmael named after the sons of Ishmael who were in the original company of Lehi and who later rebelled against Nephi along with Laman and Lemuel to become Lamanites.
Alma 17:20 And as Ammon entered the land of Ishmael, the Lamanites took him and bound him, as was their custom to bind all the Nephites who fell into their hands, and carry them before the king; and thus it was left to the pleasure of the king to slay them, or to retain them in captivity, or to cast them into prison, or to cast them out of his land, according to his will and pleasure.
Immediately upon entering the land of Ishmael, Ammon was taken captive and hauled before the king in that part of the land. It was normal for any Nephite caught in Lamanite lands to be tied up and taken to the king for him to do as he pleased which could be death, slavery or run them out of their country. It was totally up to the king as to the faith of any Nephite.