K is L’s wife’s husband’s brother. M is the sister of K. N is the sister of L. How is K related to L?

The correct choice is: “Brother”

L’s wife’s husband is L himself. So “L’s wife’s husband’s brother” is simply L’s brother: K is L’s brother (and, since M is K’s sister, K is also M’s brother). K is male, so the female relations “Sister-in-law”, “Daughter” and “Wife” are impossible. The facts about M and N are irrelevant.