Translation:They are reading a book that I like.
Is it possible to replace "which" with "that" in the tile exercises? The sentence sounds weird with "which", which is traditionally contrasted with "that" (with "which" being non-restrictive and "that" restrictive). I think it should be accepted but not suggested.
What about "They are reading a book I like"? Is it too much of a "slang"? (I'm not natively english)
Leaving out "that" is usually grammatically acceptable, so your sentence is fine, although the "that" would often be included in this particular sentence as it emphasises that you like the book.