Yes, there is only one way to get that number to go up -- by clicking the "Like" button while logged in to a valid Facebook account.
There is no way to "like" multiple times, or fake this in any way. Also, those who view the book just to see what it's about will not necessarily "Like" the book while they're on the site. Not unless they like it, that is!
To give you some idea how hard it is to tank up on "likes": one of my most popular products, Chant Compendium 3 which has sold thousands of copies, has 2 "likes" at the moment.
I have indeed posted a link to the book on many Traditional Catholic-related Facebook groups. But again, someone has to click through AND "like" the book to add to that tally. If they hate the idea, they certainly won't click the Like button.
Last night the total Likes was 230+. So about 60 Likes have come in just today. Wow.