A man narrated a story to a stranger and told him, "This girl is the wife of…

Concept:

Family-relation puzzles are solved by converting every stated relation into a generation level and a gender, building a small family tree, and then reading the relation between the two named people directly off that tree. A relation described through an intermediate person (here, "my mother") must be resolved generation by generation, starting from that anchor down to the target person.

Application:

1. Let the speaker's mother be the topmost person in the tree, F.

2. The speaker (the man) is a child of F, one generation below F.

3. "The grandson of my mother" is a son of a child of F. The statement never introduces any brother or sister of the speaker, and only a reading through the speaker's own line yields any of the four offered labels as an answer (a reading through a sibling would make the man the girl's uncle-in-law, a relation none of the options names) — so the grandson here is the speaker's own son, one generation below the speaker.

4. The statement says the girl is "the wife of" that grandson, so the girl has married the speaker's own son.

5. A person who marries one's son is, by definition, one's daughter-in-law; equivalently, the parent of the groom is the bride's father-in-law.

6. Therefore the speaker (the man) is the girl's father-in-law.

Cross-check:

Testing the remaining labels the same way, against the speaker's actual relation to the girl: a "brother" would require the girl to be in the speaker's own generation, as his sister — but the girl is one generation below, as the wife of the speaker's son; a "son-in-law" would require the man to have married a daughter of the girl, placing the girl a generation above him — but the statement instead has the girl marrying into the speaker's own family; and "son" matches the grandson's relation to the speaker (the grandson is the speaker's own son), not the speaker's relation to the girl herself. Only the father-in-law label directly matches the speaker's actual relation to the girl.

Result:

So the man is the father-in-law of the girl.