Bill asked his brother’s wife’s mother-in-law’s only husband’s only daughter to join him and his wife for dinner. What relation is she to Bill?
his sister because his brother’s wife’s mother-in-law’s = his mother, her only husband is Bill's father, and so his only daughter must be his sister
She is Bill's sister.
Bill's brother's wife's mother in law = Bill's mother
Bill's mother's daughter = Bill's father's daughter = Bill's sister