In "The Crucible," how does Proctor think Danforth is taking advantge of him?
Your question references Act IV of The Crucible when Danforth wants to use John Proctor to prove to the town of Salem that their actions against those who were accused and executed were valid.
Danforth wants to use Proctor, who is a respectable citizen in Salem, to give his court and their rulings validity and authenticity. Danforth needs John Proctor's confession nailed to the church door so that there will be no rebellious uprising in the town like there was recently in Andover, a neighboring town.
Danforth is frightened for his life, and seeks to use John Proctor to prove to the town of Salem, that there were witches in their midst, look, he is saying, even someone like John Proctor, an upstanding citizen admits to witchcraft.
One of the factors that contributed to the Salem witch hysteria was the confessions. People confessed to witchcraft so that they could save their lives. But once someone confessed, it made the existence of witchcraft more and more real.
So Danforth knows that if he uses John Proctor to prove the existence of witchcraft through his confession, no one in the town will question what the court has done, which was to hang innocent people on false charges based on the testimony of a girl, Abigail Williams, who has run away from Salem in disgrace.