This is the 1752nd most frequent Russian word.
другую
The Russian word "другую" means "another" or "other" (feminine, accusative case).
In this sentence, "другую" is an adjective that agrees with the feminine noun "книгу" (book) in the accusative case, indicating that the speaker will choose a different book.
Я выберу другую книгу.
I will choose another book.
Here, "другой" (another) describes "улице" (street) and is in the prepositional case to match its noun.
На другой улице было тихо.
It was quiet on another street.
In this case, "другую" modifies "дверь" (door) and is also in the accusative case, emphasizing a door that is distinct from the one previously considered.