Henry says that John Kwang represents a problem of the imagination for him. What does he mean?
In the book, Henry says that John Kwang represents a problem of the imagination for him because the latter doesn't live up to the stereotypical image of a Korean-American. While Henry is familiar with the introverted and reticent personality stereotypically identified with Korean-Americans, he is unaccustomed to Kwang's larger-than-life persona.
To Henry, John Kwang is a charismatic and arresting figure. Kwang doesn't seem to share the persistent wariness of American society that Henry's parents harbor. In fact, his flamboyance and confidence can be seen in the way he dresses. Kwang largely favors the American executive look but has been known to wear sensual clothing that accentuates his best features. Until Kwang, Henry had never met a Korean-American so resistant to "dilution." Kwang has the gift of putting people of all races and nationalities at ease.
From what Henry can see, Kwang isn't just a "respectable grocer or dry-cleaner or doctor but a larger public figure" who is willing to "speak and act outside the tight sphere of his family." In other words, Kwang defies convention. To all observers, Kwang is the typical politician; his is a persona accompanied by the "adjutant interest groups, the unwavering agenda, the stridency, the righteousness" that is so necessary to his position. However, to Henry, Kwang is a caricature of everything he has ever been taught about being Korean. As a result, Henry feels that he has to wrestle with his imagination to contemplate Kwang's persona as reality rather than camouflage.