Final answer:
The details indicating that Barton's establishment of the American Red Cross was meant to provide aid during both war (Detail C) and peace (Detail D) demonstrate its dual purpose for humanitarian assistance.
Step-by-step explanation:
The key details from “The Most Famous Woman in America” that best support the idea that Clara Barton established the American Red Cross to assist people during war and during peace are options C and D. Detail C: “There were only a few Red Cross rules, she explained.
The most important was that all men who were wounded in war would be cared for.” demonstrates the organization's commitment to aiding soldiers during wartime. Detail D: “It will help whenever there is a fire, flood, cyclone, hurricane, earthquake, or other disaster where it can be of use.” illustrates the organization's broader humanitarian role beyond wartime, showing its assistance during natural disasters and peacetime crises.