What's the problem and solution?
I think your question is referring to a plot analysis. As in what is the main conflict and how is it resolved? The main conflict starts right from the beginning of the book. Kit has not been born and raised in the Puritan community. She struggles throughout the book to fit in, learn their social customs, wear their clothes, meet the expected workload, etc. She is treated as an outsider. Eventually a fever/illness strikes many members of the Puritan community. Being Puritans, they believe it is the work of the devil and/or servants of the devil. Kit and Hannah Tupper (another outsider) are quickly blamed and accused of witchcraft. That's the big problem of the novel.
The problem is solved when Nat shows up in court with Prudence. He proves that Kit is not witch by providing evidence that Kit was teaching Prudence to read . . . the Bible. Kit is immediately freed and all charges are dropped. The people rejoice.