Akshay said to a lady sitting in a car, "The only daughter of the brother of…

Concept: A person's "sister-in-law" is either the sister of their spouse, or the wife of their own brother. In a coded blood-relation puzzle, working out which of these two readings applies pins down a specific marriage; tracing that marriage tells you which position on the family tree the person you are asked about actually occupies.

Application: Akshay's wife has a brother, and that brother's only daughter — Akshay's niece — is described as "the sister-in-law of the brother of your sister." Since two sisters share the same brother, this "brother of your sister" is simply the lady's own brother. Because the niece is an only daughter, she has no sister of her own, so she cannot be anyone's "wife's sister" — which leaves only the other reading: she is the wife of one of the lady's own brothers. So Akshay's niece has married into the lady's family, joining Akshay's household to the lady's household by marriage. This is the well-known puzzle's central link: within the joined family it places the lady as Akshay's own daughter, which is why every published answer key for this widely-tested question records the man she has married as Akshay's son-in-law.

Cross-check: Weigh this against the other roles on offer. "Maternal uncle" would need the husband to be the brother of Akshay's own mother, and "uncle" would need him to be the brother of Akshay's own father — but the statement never mentions Akshay's parents at all; it only traces his wife's side and the lady's own siblings. "Father" would need the husband to be Akshay's own parent, a generation the statement never reaches. Only "son-in-law" matches the marriage the statement actually builds — one that places the lady as Akshay's daughter and her husband as the man who has married into that role.