A.T. Robertson Commentary Acts 13:38

"Be it known unto you therefore, brethren, that through this man is proclaimed unto you remission of sins:" — Acts 13:38 (ASV)

Through this man (δια τουτου). This very man whom the Jews had crucified and whom God had raised from the dead. Remission of sins (αφεσις αμαρτιων) is proclaimed (καταγγελλετα) to you. This is the keynote of Paul's message as it had been that of Peter at Pentecost (2:38; 5:31; 10:43). Cf. 26:18. This glorious message Paul now presses home in his exhortation.