Complete this sentence: I think it’s cheaper if you book _____ the Internet?

The correct choice is "on," as the phrase "book on the Internet" is the standard expression used in English to refer to making reservations or purchases using online platforms. This preposition accurately reflects the action of accessing services or products through a website or online service.

Using "on" in this context signifies that the activity is occurring via the Internet, which is considered a space where various transactions take place. In contrast, other prepositions do not form customary phrases related to online bookings. For example, "in the Internet" or "for the Internet" are not commonly used, and while "to" suggests direction or intent, it does not fit the context of online booking in the same way that "on" does.