I received a book review request from a publishing company called PACKT. How do I know if the company and book is credible and if the effort would be worthy?
Why do you care? Let them send you the book, if you are at all interested in the topic. (Free books! Yay!)
Then review it. If the book is obviously crap, then stop reading after page 15, write up how far you got and why you stopped reading, and submit the review. You may not get any more requests for reviewing from that particular publisher after that, but a one-paragraph review that warns people off a bad book is certainly helpful. And the entire process won't cost you more than half an hour.
And if the book is good, you can spend more time on it, write a thoughtful review and got a Free Book out of it.
EDIT: on second, third or more-th glance, I do see a way in which reviewing for a shady publisher can hurt you. Suppose an author plagiarizes a large amount of text for his book - but you don't notice (maybe because you are not familiar with the text that was plagiarized) and write a good review. Once this becomes known, of course people will wonder why you did not notice.
This really presupposes that something like this could more easily happen with a shady publisher, an assumption which may be open to question itself. I'd rather wonder about the author than the publisher here.
So I'd recommend something like this: google the author. Check his publications. Does he have a track record in the field? I'd be suspicious if someone with no scientific footprint suddenly were to write a book.
Check the publisher. What else have they published? Go by the publisher's website and by Amazon, especially if you don't trust them to be honest on the website. How are the reviews of their other books on Amazon? If you google their books' titles with "site:edu", does any educational institution set them as textbooks?
Finally, if the author has a website but does not mention the book you are supposed to review and the publisher looks extremely fishy to you, write him an email and ask about the book. It may be that an unethical publisher put his name on a plagiarized book that he never saw (however, I don't think that this is likely).