She is reading the first book that belongs to her, rather than someone else's book?
It would typically be understood as the first book she's reading, regardless of owner or author.
Thanks for the explanation
Kan man si hennes istedet for sin her? Or does that lead to the other meaning the op suggested?
It would mean that she is reading another girl/woman's first book. The first book of a female author, for example.
Regular speed it says "sheen", slow "seen" (for sin)
This is because the r and s er next to each other.