Or by her participating that she is knowingly involving herself in a scam. Which, yeah, it's just books - but it's pretty obviously a pyramid.
No shame if you don't see how it's a scam, the cozy blanket and glass of wine are meant to throw you, and they chose 36 because it's a confusing enough number where you don't think too much about how it grows.
She gives one book to her upline. She then sends out post to 36 more people to give her 36 books. Each one of them then needs to find 36 people each, which is now 1296 people in that level if they each want 36 books. Thus the exponential pyramid. Of course there is zero way each of them will find that many people, let alone the levels below that. It's a scam that benefits those higher up, and the ones lower will likely not receive anything.
Of course she sees nothing wrong with that. She said "Sometimes I get books, sometimes I don't, that's just part of the game". Which... it's not a game when it's real money being passed around.
On top of that, whenever we see a pyramid scheme we should be stamping it out - hard. Folks, please spot the signs and point them out. Don't be afraid to comment on posts calling them out as scams.
Edit: To be clear the idea of a growing book exchange isn't a bad one, as explained in the comments though the way to make it not a scam is to make it 1:1. You either send a book and receive a book, or if they like the 36 number, you change it to "I'll send a book to whoever sends me a book!". Then it's a true book exchange.
Your math is correct.