The correct answer is B. arrogant.
A brash person is someone who is rude and aggressive, especially in a way that shows a lack of respect for other people. An arrogant person is someone who has an exaggerated sense of their own importance or abilities.
The new officer is described as being a brash young man. This means that he is likely to be rude and aggressive, especially in a way that shows a lack of respect for other people. He may also have an exaggerated sense of his own importance or abilities.
The other options are not as likely to be true of the new officer. A polite person is someone who is courteous and respectful. A kind person is someone who is generous and compassionate. A handsome person is someone who is attractive. It is possible that the new officer is any of these things, but it is more likely that he is arrogant.