In the book The Witch of Blackbird Pond, what does Mercy ask Kit's help with?

Mercy asks Kit to help her teach school.

There is a big learning curve for Kit in Wethersfield.  It takes her some time to learn the chores of the house and the customs of the people.  She helps out wherever she can.  One day, Mercy tells her that she has been offered a position helping Mercy teach school.

"The most wonderful thing, Kit! Dr. Bulkeley has recommended to the selectmen that you help me with the school this summer." (Ch. 8)

Kit had no idea that Mercy even taught school.  It turns out that she teaches at the “dame school” for younger children during the summer months.  She teaches them to read and write, and then when they get old enough they go to the grammar school.  Mercy's school is right there in the kitchen.

Kit is not sure about teaching, since she has never done it.  Mercy tells her that she is indeed qualified.

"I don't know much about children," said Kit dubiously.

"You know how to read, don't you? John Holbrook told Dr. Bulkeley you can read as well as he can." (Ch. 8)

This surprises Kit too.  Of course, being able to read and being able to teach are two different things.  Kit still does not quite fit into Wethersfield society.  Her education was much different than theirs, because in Barbados the culture was very different.  Kit read Shakespeare there, not just the Bible.  The people of Wethersfied do not approve of such reading.

Mercy tells Kit that they both will be earning wages, and that Kit will help a great deal.  She finds the texts boring and monotonous, and it tests her patience.  Remembering back to her own education, Kit decides to make up her own lessons with her pupils like her grandfather did with her.  She makes up rhymes with the children’s names and has them read them.  The kids love it, hanging on her every word.

Kit had no idea that her methods were novel and surprising. She only knew that the past ten days since the dame school had begun had been the pleasantest she had known in Connecticut. (Ch. 9)

Kit enjoys teaching and gets along well with the children.  Kit even tells the children stories, which Mercy worries is an “indulgence.”  One day she has the children act out the story of the Good Samaritan, since they already know it.  For this, Kit gets in trouble with the schoolmaster, who disbands the school and fires them both.  Kit finally gets Mr. Kimberley to give them one more chance, and then uses much more orthodox methods.

Most of us today would find no fault with Kit's methods, but Puritans would have found them scandalous.  Everything was simple and proper, and play-acting was clearly forbidden.  Kit had no idea that she was doing anything wrong, because she thought that the story being from The Bible would make it acceptable.