Answer: B) To win her hand in marriage.
Step-by-step explanation: a sentence fragment is a group of words that form a dependent clause (it doesn't make sense on its own), in order to be a complete sentence, it has to be at least one independent clause (a phrase that has a subject, a verb and has meaning on its own). In the given paragraph, the phrase "To win her hand in marriage" is an example of a fragment (it is a dependent clause without a subject).