Q: Why should you check the reputation of the publisher of a book?

There are two aspects to your question. One is the actual question itself. The other is the part on critical thinking.

To respond to the second one first, because this requires you to engage in critical thinking, it wouldn’t be fair to provide the answer. You would need to (as the purpose of the exercise goes) read up on book publishers, what makes for quality publishers, and what makes for low-quality publishers in order to form your response.

Having said that, and to respond to your first question, it is important to know the reputation of a book publisher because it may impact your reputation too in case you decide to publish with them. A low-quality publisher may reflect badly on your abilities to both write for and to select the right publisher. A high-quality publisher would, on the other hand, add to your credentials as a writer.

As we are talking about books, quality literature, and developing critical thinking, and also for your exercise, you need to begin by reading up relevant other literature. In that case, you’ll find this resource helpful: Tips for effective literature searching and keeping up with new publications

Hope that helps. And all the best for your assignment!