Beneatha, a 4w3, dreams of being a doctor and discovering who she really is by avoiding assimilation and reconnecting to her roots. Her journey is both "forward" and "backward," in the sense that she is reaching higher professionally than others in her family have done before (forward) while simultaneously reaching further "backward" to explore African culture. Her identity crisis is of course bigger than just her character — the tension between assimilation and reconnecting to African roots is a major theme of the movie, further embodied by her two courters — George, a preppy college boy who goes to the theater and assimilates into white culture; and Joseph Asagai, who is so "African" that Mama can't even pronounce his name. And of course, Mama is so much an American now, 5 generations deep in this country, descended from slaves, and uneducated, that she doesn't have much of an interest in her African roots. Anyway, Beneatha, a 4w3, is overtly trying to be “true to herself.” She spurns assimilation even as she aspires to become a doctor and she experiments with various forms of self-expression such as theater and guitar. She delights in trying on a Nigerian outfit and becoming a "Queen of the Nile." Her 3 wing makes her ambitious, not settling to be just another laborer like the other members of her family. But her 4-ish “I am going to be myself” theme dominates.
^ I wrote this a while ago and feel that her “finding herself” journey is more attachment.. but I don’t see her as a core 3 or 9, and I don’t know how I would justify 6.