This is a bit of an odd question. I'm supposing what your teacher is really asking about is characterization: How is characterization developed in changing relationships, especially between Elizabeth and Darcy? I'm supposing this because the simple and direct answer to the question as posed is: Through characterization. So, supposing that I am correct in supposing the objective is an analysis of characterization, let's proceed on that route.
First, let's take a quick look at the changing relationship between Charlotte and Elizabeth, which has a few more direct and compact instances of characterization that illustrate the techniques Austen uses:
- personal confidences
- realization of differences of opinion
- realization of erroneous understanding
- adjustment to new circumstances that may or may not be approved of
While a change in their relationship is foreshadowed in their conversation during which Elizabeth expresses her disbelief in Charlotte's idea of marrying without love ("... Charlotte; but it is not sound. You know it is not sound, and that you would never act in this way yourself" (Ch 6)), the change in relationship actually comes when Charlotte expresses to a surprised Elizabeth her reasons for accepting marriage with Collins.
"I see what you are feeling," replied Charlotte, "... I am not romantic, you know. I never was. I ask only a comfortable home; and considering Mr. Collins's character, connections, and situation in life, ..."
Elizabeth quietly answered ... and after an awkward pause, they returned to the rest of the family. ... Elizabeth was then left to reflect on what she had heard. ... She had always felt that Charlotte's opinion of matrimony was not exactly like her own, but she could not have supposed it possible that, when called into action, she would have sacrificed every better feeling to worldly advantage. ... to the pang of a friend disgracing herself and sunk in her esteem, was added the distressing conviction that it was impossible for that friend to be tolerably happy .... (Chapter 22)
In this scene we see that Charlotte personally confides in Elizabeth and that there is a mutual (though particularly for Elizabeth) realization of a difference of opinions, especially notable when Elizabeth exclaims: "Engaged to Mr. Collins! my dear Charlotte, -- impossible!" We then see Elizabeth's realization of her erroneous understanding of Charlotte's ideas and convictions. Later, we see both young women adjusting to their new relationship in circumstances that Elizabeth does not approve of when Charlotte invites her to and Elizabeth goes to visit at Charlotte's new home in Kent at Rosings.
Austen uses the same techniques to characterized the changing relationship between Elizabeth and Mr. Bennet and, more particularly, between Elizabeth and Darcy. Since the interactions between Elizabeth and Darcy are spread out through the entire book, there isn't a neat encapsulation as we find for Elizabeth and Charlotte, but we can isolate an illustrative example that can guide your further examination of their changing relationship. A good place to look is the unexpected encounter between Elizabeth and Darcy at Pemberley.
Mrs. Reynolds has been instrumental in energizing Elizabeth's realization of erroneous understanding relating to Mr. Darcy, a process begun with his presentation of confidences shared in his letter to her, given at Rosings Park just before Darcy's sudden departure. When Elizabeth and Darcy chance to meet at the entrance to his park walks, Darcy is at pains to present himself in a new light resultant upon the realizations wrought upon his mind by the confidences Elizabeth shared relevant to his ungentlemanly deportment: "had you behaved in a more gentlemanlike manner."
Amazed at the alteration in his manner since they last parted, every sentence that he uttered was increasing her embarrassment; and every idea of the impropriety of her being found there recurring to her mind, the few minutes in which they continued together were some of the most uncomfortable of her life. (Chapter 43)
After the exchange of heated confidences, hers verbal, his written, and after realizations of their erroneous understanding, they meet again and adjust to new circumstances that they both approve of.