Final answer:
In the context of the question, 'broach' is a verb that means to bring up or initiate discussion about a subject, making option D. 'mention' the correct synonym.
Step-by-step explanation:
The word broach most nearly means to mention or bring up (a subject) for discussion or debate. It is often used when referring to a topic that is difficult or sensitive, and one needs to introduce it carefully into the conversation. Therefore, the correct answer to the question is D. mention.
For example, if someone says, 'Let's not broach the subject of politics during dinner,' they are suggesting not to bring up or mention the topic of politics.