It's a great question, but a little bit tricky to answer. The reason is that neither of them is wrong, in other words, you can use both of them, but "책 읽기" sounds more natural and it is economical, too.
나는 책 읽기를 좋아합니다. I like reading a book. My hobby is reading a book.
나는 책을 읽기를 좋아합니다.
The latter sounds more emphatic than the former, but doesn't sound as natural as the former or
나는 독서(讀書)를 좋아합니다.
"독" means to read and "서" means a book. If there is a Korean word composed of Chinese characters, people, especially adults, tend to use more those words than such words as "책 읽기".
One more thing to note is if the first word is composed of more than two characters, it is not common to use "을" or "를" after it. It doesn't mean you can't use it. For example,
나는 영화 보기를 좋아합니다. I like watching a movie. My hobby is watching a movie.
나는 영화를 보기를 좋아합니다. (?)
It does make sense, but sounds weird.
If you really want to use "을" or "를", you can change the form and use "~ 하는 것", for example,
책을 읽는 것, 영화를 보는 것.
Both of them sound as natural as 책 읽는 것, 영화 보는 것.