Pointing to a girl in photograph, X said: "She is the daughter of my paternal…

Concept

In blood-relation puzzles, a family word is resolved by first pinning down every intermediate person named in the statement, then tracing the relation forward step by step from the speaker to the target person. A constraint such as "only son" rules out every alternative for that role, forcing it onto one specific relative.

Application

1. X's paternal grandfather has exactly one son (given as "only son").

2. X's own father is, by definition, one of the paternal grandfather's sons.

3. Since the paternal grandfather has only one son, that son cannot be anyone but X's father.

4. The girl in the photograph is the daughter of that son — that is, the daughter of X's father.

5. A person who is the daughter of X's father (and is not X) is X's sister.

Cross-check

Running it in reverse: if the girl is X's sister, then from X's point of view she is indeed "the daughter of my paternal grandfather's only son," since that only son is exactly X's father. The statement holds consistently both ways.

So, the girl is X's sister.