The best answer is:
- His admiration of her work displays her eagerness for approval by others.
In the passage, the American's appreciation for the young lady's artwork prompts her to engage with him about the sale. His persistent questioning about the price (using "Combien?" and "How much?") highlights her desire for his approval and recognition of her artistic talent. The way she initially seeks to appear indifferent and then takes the opportunity to demonstrate her skills (both in her painting and in negotiating the price) suggests her eagerness for validation of her work from someone who admires it.