how does it work? (the multiplication)

Becaus ln(A*B) = ln(A)+ln(B), you need 2 sliding elements and you work in logarithmic scale. Look at "slide rule"[0], this is really nice stuff.

[0]: https://en.wikipedia.org/wiki/Slide_rule

Are you asking how the bracelet multiplies two numbers? It's the same idea used by slide rules -- you take the logarithm of the two numbers, then add the logarithms instead of multiplying -- same result, with somewhat less accuracy depending on available decimal places.

This method was widely used in the pre-computer era to save time in calculations. Tables of logarithms (and slide rules) were a mathematician's best friend.