In chapter 6, why does Daisy say she's giving out "gren" cards?
In chapter 6, Daisy Buchanan is attending yet another of Gatsby's lavish parties. She's giving out green cards, which she's using as a kind of ice-breaker, something that will enable guests to get acquainted with each other. You take a card, approach another guest at the party, and that entitles you to a chat, a kiss or a dance. It's a novel way for people to get to know each other:
"If you want to kiss me any time during the evening, Nick, just let me know and I’ll arrange it for you. Just mention my name. Or present a green card. I’m giving out green—"
It's revealing that, in this extract, Daisy is suddenly cut short by Gatsby. For him, the green card acts as an unwelcome reminder of the true nature of their relationship; the "green light" at the end of the dock to which he stretches his arms, but which quickly disappears. The green card represents for Gatsby the fact that Daisy is unobtainable, and that the only way he can be with her is through artificial means such as green cards and the shallow social gatherings at which they're given out. The green card is a ticket, an invitation to Daisy's love. But Gatsby won't take one; he wants to maintain appearances as the reality of his thwarted love for Daisy is just too hard for him to accept.
I believe that the "green cards" are a reference to dance cards, which were a social custom at the time. When a woman attended a party where dancing would occur, she could hand out cards to men with whom she would like to dance. Another similar custom was a dance card or booklet that she kept, and potential dance partners asked to sign it so that they could dance with her. This custom is very different from modern dance behavior. The color green reinforces Fitzgerald's use of that color to represent hope and wealth as in the green light at the end of Daisy's dock. Daisy comes to Gatsby's party eager to have a good time, of course, but she also looks forward to seeing Jay in a very public place where their private behavior may go unnoticed. She's almost giddy with excitement because she offers Nick a card, telling him he can exchange it for a kiss, which would be, from Nick's perspective, pointless.