In "The Crucible" what is Reverend Hale doing that brings “hope” and how does that tie to Danforth thinking that he has been preaching in Andover?
Hale is going to each of the prisoners who have not confessed to witchcraft, and trying to help convince them that if they lie to save their life, it isn't that big of a deal, and that "God damns a liar less than he that throws his life away for pride." For many people in the jails who have been refusing to lie, because for all of their lives they have been taught that "God damns all liars", this might be a ray of hope for them, a way out of the awful situation that they have found themselves in. For a minister, a man of god, to come to them and tell them that it is okay to lie, that in fact NOT lying is the bigger sin, it would be a great burden lifted off their shoulders. He tries this argument with Elizabeth, stating that "life is God's most precious gift; no principle, however glorious, may justify the taking of it."
Danforth and others suspect he has been preaching in Andover because he is going against the courts here, so why not there too, and in Andover there have been rumors of rebellion. So, they attribute the rebellion to Hale and his ministry of "hope." Hale denies this claim, stating that "Thank God they have no need of me in Andover".