I believe the conflict you are asking about is the one that occurrs when Laurie invites the older girls, Jo and Meg, to the theater to see the play Seven Castles. Amy, who has not been invited, figures out where her sisters are going, and begins to whine and cajole to be taken along. Amy, who is used to getting her way, insists that she will go, because she has her own money, and Mother has said that she might see the play, although not necessarily with Meg and Jo. Meg begins to waver, saying that perhaps the girls can take Amy along, but Jo is unyielding. Jo argues that it would "be very rude, after (Laurie) invited only (her and Meg,) to go and drag in Amy." Jo does not look forward to the prospect "of overseeing a fidgety child when she want(s) to enjoy herself," and she also says that, since the seats are reserved, Laurie would chivalrously give his seat up for Amy and be the one to sit alone, which will spoil their pleasure. Laurie then arrives, and Jo and Meg go with him, leaving Amy behind, wailing and promising that she will make Jo "sorry for this."
Amy does indeed make Jo sorry; although she does not understand the full implications of her act, she does the one thing which she knows will hurt Jo severely. Amy takes the book that Jo has been working on, the one which holds the only painstakingly written copy of her literary creations, and burns it (Chapter 8).