Answer: D. She had made up her mind; she was going to travel the world one way or another.
Explanation: The most common uses of semicolons are, when using conjunctive adverbs (however, therefore, finally, likewise, etc) to join two independent clauses, we place the semicolon before the adverb (option C is incorrect because "however" isn't joining two clauses), and the other common use is to join two related independent clause without the use of any conjunction like "and," "but" or "or" this is the case of the option D, we have two related independent clauses " She had made up her mind" and "she was going to travel the world one way or another" joined by a semicolon.
