The idea behind Facebook promotions is simple:
The link to your e-book’s sale page will be posted on up to 100 different Facebook groups and pages dedicated to writing, e-book promotions, authors and more. The combined member count in those groups is roughly one and a half million users (1,500,000+).
In addition, I will find niche specific groups relating to your book and promote it there as-well. (However, I cannot estimate the number of such niche groups or their member sizes before I know what your book is about.)
Promoting your e-book on Facebook is one of the simplest ways of getting the information about your book in front of hundreds of thousands of eyes.
However, it is important to note that success hinges largely on the presentation and the popularity of your book’s topic. Uninspired titles, amateurish covers and poorly written descriptions are the main reasons why your book may be ignored, despite its great content. Unfortunately, people do judge a book by its cover.
In general, Facebook promotions tend to be most effective for Free to download e-books. So if your book is permanently free or in its Amazon KDP Select free promo, you can definitely get a good amount of extra downloads. The promotion is noticeably less effective for paid books, but depending on the amount of profit you make from a single sale or Kindle Unlimited borrow, it may still be worth it.
Unfortunately guaranteeing results is impossible. All I can promise is that your book link will be posted during optimal times (US time zones) and will be visible to thousands of Facebook users.