Final answer:
Elizabeth feels goodwill and gratitude towards Darcy as he discreetly helped her family by resolving Lydia's elopement issue, demonstrating generosity and kindness.
Step-by-step explanation:
In chapter 44 of Pride and Prejudice, Elizabeth Bennet's feelings towards Mr. Darcy are complex, but she feels goodwill and gratitude towards him primarily because he has been generous and kind to her family. This generosity is highlighted through his involvement in resolving the crisis related to Lydia's elopement with Wickham, which threatened the reputation and future prospects of the entire Bennet family.
Darcy's actions, which were done discreetly and without seeking recognition, displayed a sense of responsibility and care for Elizabeth and her family's wellbeing, hence earning her gratitude.