The religious leaders sent spies to keep a close watch on Jesus. The spies pretended to be honest. They hoped they could trap Jesus with something he would say. Then they could hand him over to the power and authority of the governor.
References for Luke 20:20
So the spies questioned Jesus. "Teacher," they said, "we know that you speak and teach what is right. We know you don't favor one person over another. You teach the way of God truthfully.
Is it right for us to pay taxes to Caesar or not?"
Jesus saw they were trying to trick him. So he said to them,
"Show me a silver coin. Whose picture and words are on it?"
"Caesar's," they replied. He said to them, "Then give to Caesar what belongs to Caesar. And give to God what belongs to God."
They were not able to trap him with what he had said there in front of all the people. Amazed by his answer, they became silent.