4:2 Being grieved that they taught the people, and preached through Jesus the resurrection from the dead.
Peter and John were preaching Jesus. They were preaching Jesus and faith in Him unto eternal life. They were preaching His resurrection, and how that would ensure the resurrection of believers, and the coming earthly Kingdom promised to the nation of Israel. There is, however, no mention here of the cross of Christ Jesus; no mention of Jesus's sacrificial death, of Jesus being delivered for our offences and raised for our justification. It is the gospel of the Kingdom plus the resurrection of Christ, which is the gospel of the Circumcision, being preached.
4:10 Be it known unto you all, and to all the people of Israel, that by the name of Jesus Christ of Nazareth, whom ye crucified, whom God raised from the dead, even by him doth this man stand here before you whole.
Peter is preaching the gospel of the Circumcision and the assurance of the coming Kingdom thru Christ's resurrection. He is still preaching faith in the name of Jesus, that Jesus is the Son of God and the Christ. Israel had to believe on Jesus to have eternal life; it was then required that they confess him, be baptized, and keep the law to enter the coming earthly Kingdom of Heaven.
4:12 Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.
Naming Jesus as the Christ, the Son of God was required for Jews to have eternal life. Although verse 12 is to the Jews, it is also for us. We can also acknowledge that it is only thru faith in Christ Jesus alone and His provision alone for our,forgiveness, justification, and righteousness unto eternal life.