Final answer:
The best synonym for 'will comb the shelves to find that book' is 'search the shelves to find that book', as it specifically refers to the act of looking for a book.
Step-by-step explanation:
The synonym for the phrase 'will comb the shelves to find that book' is most accurately represented by search the shelves to find that book. This implies looking through the contents of the shelves meticulously to locate a specific book. In contrast, phrases such as organize, clean, or arrange the shelves imply different actions that do not exclusively focus on the act of finding a specific book but rather on ordering or tidying the shelves themselves.