They had a clever approach but it was filled with
deceit.

The Jewish people were weighted down with the
tax burden. And the Israelites were grieved by
the fact that they were the chosen nation but
had to pay taxes to a heathen.

Coming to Jesus the Herodians said, "We know
that thou art true, and teachest the way of God
in truth, neither carest thou for an man; for
thou regardest not the person of men."
Matthew 22:16

They were trying to get Jesus to give them His
opinion (like they were looking for guidance) on
if they should or shouldn't pay their tribute.