The abstract noun "disagreement" can be stated as the verb "disagree." AT: "They strongly disagreed with each other" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
To entrust to someone means to place the care and responsibility for someone or something to another person. This can be stated in active form. AT: "after the believers in Antioch entrusted Paul to the grace of the Lord" or "after the believers in Antioch prayed for the Lord to take care of Paul and show kindness to him" (See: [[rc://en/ta/man/translate/figs-activepassive]])
The previous sentence implies that Silas was with Paul. AT: "they went" or "Paul and Silas went" or "Paul took Silas and went" (See: [[rc://en/ta/man/translate/figs-explicit]])
Encouraging the believers in the churches is spoken of as though Paul and Silas were making the believers physically stronger. The word "churches" refers to the groups of believers in Syria and Cilicia. AT: "encouraging the believers in the churches" or "helping the community of believers to depend even more in Jesus" (See: [[rc://en/ta/man/translate/figs-metaphor]] and [[rc://en/ta/man/translate/figs-metonymy]])