Why were the Sadducees most concerned about Peter's preaching in Acts 4?
The Sadducees denied any resurrection from the dead, holding that people lived and died like animals. Peter's preaching that Christ was alive and could yet return as King directly contradicted their doctrine, so they were grieved and challenged him for teaching something that flew in the face of their belief.
Les explains that in Acts 4, as Peter and the others spoke to the Jewish people, the priests, the captain of the temple, and the Sadducees were grieved because they taught the people and preached through Jesus the resurrection from the dead. He notes that the Sadducees were Jews, not Gentiles, and their doctrine was that there is no resurrection from the dead—you lived like an animal and died like an animal. Therefore, the group most concerned about Peter's preaching that Christ is alive and is yet able to come and be their King was the Sadducees, because it directly contradicted their belief. They came at Peter, saying, in effect, how dare you teach something that flies in the face of our doctrine—there is no such thing as someone coming back from the dead.