Question

Which detail from A Story of the Red Cross shows Clara’s purpose for writing it?

To say that we were kindly and gratefully received by them says nothing that would satisfy either ourselves or them.
We were asked not only to act with them, but to assume charge of the administration of relief.
I have dedicated this little volume to the people with whom, and for whom, have gone the willing labors of twenty-five years—initial labors, untried methods, and object lessons.
This is a tedious story; but if gone through, one has a little insight into the labor of a Red Cross field of relief.

Answer 1

"I have dedicated this little volume to the people with whom, and for whom, have gone the willing labors of twenty-five years—initial labors, untried methods, and object lessons."

This sentence explicitly states her purpose: to present and dedicate the book to those she worked with and to share the lessons and methods from her 25 years of work.