Can you explain the story of the woman who wanted to fast, as introduced in Chapter 32?

Certainly. Chapter 32 introduces the story of a woman who had a strong desire to have Sai Baba's darshan. Her plan was to stay for three days and observe a strict fast without any food. However, the chapter explains that an occasion arose where her firm resolve was broken by Baba himself. Instead of letting her fast, Baba arranged for her to make and eat puranpolis to her heart's content. The underlying lesson, as stated in Chapter 32, is that "wearing out the body for others' sake - this blessed act is true welfare." This incident was used to teach her that selfless service is a higher virtue than the physical austerity of fasting.