The man has chromosomes X and Y. He must have received the Y chromosome from his father and the X chromosome from is mother.
Since the condition is only carried on the X chromosome, his mother must carry the recessive allele.
His daughter must have the chromosomes X and X. The daughter must have received one X chromosome from her father (the man in the question) and one from her mother. Therefore, she must also carry the recessive allele.
So D is correct.