After they failed to question the authority of Jesus, his enemies tried to turn the people against him. From the beginning, it is clear that the Pharisees and the supporters of Herod (see 3:6) were not sincere. They were trying to trap Jesus so he would say something that could lead to his arrest.
The question Is it lawful to pay taxes to Caesar or not? was carefully planned. It put Jesus in a difficult situation where any answer seems wrong. If he said yes, the people might turn against him, because they hated Roman rule and taxes. If he said no, he could