Complex sentence: Throughout the book, the author suggests that the way past "the Negro Problem" in general, and these three manifestations of it in particular, is for both Negro and white America to transcend what they think they know, believe, understand and fear.
Split into simpler sentences: Throughout the book, the author suggests that the way past the Negro Problem. In general, both Negro and white races must transcend what they think they know, believe, understand and fear.