If H is the daughter of R, R is the father of S, S is the son of T, T is the daughter of N, then how is H related to N?

H is R's daughter; R is T's son (since S is R's son and T's child, T is R's parent); T is N's daughter. So R is N's grandson and H is N's great-granddaughter — but tracing the female line: T is N's daughter and H is T's son R's daughter, making H N's daughter's son's daughter, i.e., daughter's daughter (granddaughter).