This is a yes/no question which means you should raise your eyebrows for the whole question. Zoée is asking this using the simple yes/no structure (YOU LIKE BOOK READ YOU?) but you can also use a more topicalized structure such as BOOK READ LIKE YOU? or BOOK READ YOU LIKE? (you would still keep your eyebrows raised for the whole question).
You might be wondering why it is BOOK READ and not READ BOOK - you *can* use READ BOOK (and you will see lots of Deaf people sign in this order) but generally you would first state what and then the activity. Another example would be "Do you like washing dishes?" - in this case, it would be DISH WASH.