"She reads your books."
Translation:Hon läser dina böcker.
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Short version: both are correct translations.
English uses you for both singular you and plural you, Swedish differentiates between the singular du and the plural ni. The possessive form of you in English is your, whilst in Swedish it's din / ditt / dina for en-words / ett-words / plural (referring to several owned things) when there is just one owner (possessive du), and er / ert / era for multiple owners (possessive ni).
Din bok = Your (one person's) book. Bok is an en-word.
Ditt piano = Your (one person's) piano. Piano is an ett-word.
Dina böcker = Your (one person's) books.
Dina pianon = Your (one person's) pianos.
Er bok = Your (several people's) book.
Ert piano = Your (several people's) piano.
Era böcker = Your (several people's) books.
Era pianon = Your (several people's) pianos.
The sentence is to be translated from English to Swedish, hence either dina or era works, as the English sentence doesn't specify if it's a single or multiple owners, and there is no context given that could tell you that.
It probably gave you "era" as the correction because it was the closest correct answer to what you had put.
It has to be either "era" or "dina" because there's more than one book. It can be either of those, because we don't know if we're addressing one person (dina) or multiple people (era).
When talking to one person:
- use din before singular en words
- use ditt before singular ett words
- use dina before plural words
When talking to more than one person:
- use er before singular en words
- use ert before singular ett words
- use era before plural words
"Böcker" is plural, so you have to use either dina or era.