Jay Gatsby has two significant meetings with Daisy in F. Scott Fitzgerald's The Great Gatsby: when he meets her for the first time and when he meets her again five years later. The first meeting is barely mentioned in the novel, so I assume you are referring to the second meeting between Gatsby and Daisy which happens in chapter five.
In the past five years since he last talked to Daisy, Gatsby has worked almost desperately to earn enough money to be somehow worthy of her love. He has moved into a mansion directly across the bay from her and has been throwing elaborate parties hoping she might just show up at one of them, but she has never appeared. Now that he has met Nick, Daisy's cousin, Gatsby decides to take decisive action. He asks Jordan Baker to ask Nick to ask Daisy to come to Nick's house for tea. These are Gatsby's actions; for this assignment you will, of course, have to write what he is feeling in what you believe to be Gatsby's tone and words.
Gatsby feels anxious, excited, and nervous about seeing the woman he has loved for so long, and he is eager for everything to be perfect. Once there is nothing more to do but wait, Gatsby sits nervously until two minutes before Daisy is scheduled to arrive; the waiting is more than he can bear and he abruptly leaves in the rain.
Gatsby must have been waiting somewhere nearby; perhaps he just needed to be able to collect himself in private after seeing her in person after so many years of longing. (It must be an overwhelming experience to have such a powerful dream finally come true.) Once Daisy is inside, Gatsby has calmed himself enough to appear at the door, but he seems quite miserable.
He is stiff and brusque in his nervousness, and the longed-for meeting between Gatsby and Daisy is awkward and abrupt. In fact, Gatsby catches Nick alone in the kitchen and says:
"This is a terrible mistake," he said, shaking his head from side to side, "a terrible, terrible mistake."
It is clear to Nick that Gatsby just has too many feelings to express effectively, so he reassures his new friend and then leaves. [Exactly what happens when Nick leaves cannot be found in the novel, so it may be something interesting for you to imagine and write for this assignment.] When Nick returns, the rain has stopped outside and everything is different inside.
Now that Gatsby and Daisy have gotten beyond the awkwardness, Gatsby wants to show Daisy everything he has acquired. As he shows her his house and everything else she wants to look at, Gatsby is filled with pride because he knows Daisy will admire him for what he has accomplished since they were last together.
Nick observes that Gatsby
had passed visibly through two states and was entering upon a third. After his embarrassment and his unreasoning joy he was consumed with wonder at her presence. He had been full of the idea so long, dreamed it right through to the end, waited with his teeth set, so to speak, at an inconceivable pitch of intensity. Now, in the reaction, he was running down like an overwound clock.
After Daisy leaves, Nick can see that Daisy has not quite lived up to Gatsby's unreasonable and idealistic expectations of her and their meeting. No one could have lived up to the illusion Gatsby had created.
To write about this emotional meeting from Gatsby's point of view, you should use language which reflects his doubts and fears as well as his hope and love.