Remember, in literature, complications are the difficulties encountered by characters which form the action of the plot. Little Women is a long enough novel that it involves several different conflicts and complications. Looking at the themes of the novel might help you identify different parts of the plot that would be considered complications.
One of the major themes of the book is that of gender roles and the fact that the book focuses on four women as the protagonists during a social and historical time when women were not considered equal to men in things like money, land ownership, business, and education. A complication these girls repeatedly run into (especially Jo) is the struggle to find a voice and an identity in a male-dominated society.
Another theme of the book is wealth versus poverty. Though the March girls are happy, healthy, and seemingly well taken care of, they are not wealthy. They are not so poor that they cannot give to others, but they are by no means as rich as the Laurences. This class dynamic results in several complications in the novel. First, it becomes a complication when Laurie falls in love with Jo and later Amy. Wealth also creates a complication among the sisters as they discover the differences in what they want in life and compare themselves to others.
Other specific details of the story that could be considered complications are Beth's death and Jo's decision not accept Laurie's proposal.