Question

What motivates the stranger to ask elisa about her chrysanthemums

Answer 1

His desire for money.

Answer 2

The stranger asks Elisa about her chrysanthemums motivated by his desire for money.

The stranger is a tinker, in other words, a person who goes from one place to another, mending metal objects such as pots and pans. As part of his job, he  has to demonstrates his skills to the people he meets on his journeys, and like any good salesman, he needs to be able to meet his potential customers' needs if he's going to make that sale.