This will be challenging because there are several layers of ambiguity present.  The first is the premise of "knowing thyself," to borrow a Transcendental bromide.  Whether or not anyone "knows themselves" and how one demonstrates they do or do not know themselves is a challenge to prove.  Outside of this would be the perception of the man, himself.  There will be some who will debate this point out of dislike or support of the individual.  To have to filter these two levels out in assessing answer is going to be difficult.  If one was to take the vision presented in Dreams from My Father, it might help in assessing the statement because of the limits set.  The issue of how one deals with race and its impact on one's identity might be how the statement can be addressed with knowing oneself.  That is to say, that Obama has addressed that the issue of race and ethnicity are challenging elements in attempting to define oneself.  Once an individual has understood the implications of these forces on one's identity, then the individual has a better chance of understanding the full dimensions of one's identity construction and stands a better chance of success.  The memoir does display this to a strong extent, in that individuals who are of "the other" have to endure a bit more reflection to understand how race and other social constructions impact who they are and how they are perceived.  Understanding the role of his father both in his life and outside of it, the function of his mother, and his raising by his grandparents, as well as how society viewed him and how he viewed himself are all parts of what Obama defines as "knowing himself" in the narrative.  Through this reflection and rumination, it is apparent that he understands more of himself and can place himself in a position to succeed.