"Book reading" is a noun phrase. It is the activity of reading a book. "Reading book" is not grammatical. There needs to be an article. I am reading a/the book. In this sentence "reading" is a present participle (part of a compound verb). In the simplest terms: one is a noun and one is a verb if it was corrected with an article.

"Book reading" is not a common phrase. You could use it, I suppose, as "I like book reading" where book reading acts as a noun, but it sounds awkward. "Reading a book", however, is a common and correct phrase that makes use of reading as a verb.

Reading a book is a good way to pass the time. Book reading is a good way to pass the time. I really enjoy reading a book. I really enjoy reading books. I teally enjoy having a book to read.

Answer below.