en_tn/act/13/38.md

let it be known to you

"know this" or "this is important for you to know"

brothers

Paul uses this term because they are his fellow Jews and followers of Judaism. They are not Christian believers at this point. Alternate translation: "my fellow Israelites and other friends"

that through this man forgiveness of sins is proclaimed to you

This can be stated in active form. Alternate translation: "that we proclaim to you that your sins can be forgiven through Jesus" (See: rc://en/ta/man/jit/figs-activepassive)

forgiveness of sins

The abstract noun "forgiveness" can be translated with the verb "to forgive." Alternate translation: "that God can forgive your sins" (See: rc://en/ta/man/jit/figs-abstractnouns)