This is the 4890th most frequent Russian word.
какую
"Какую" means "which" or "what" (feminine, accusative form).
Here, 'какую' is the accusative singular feminine form of 'какой' (which). It is used as a question word to inquire about a specific book.
Какую книгу ты прочитал вчера?
Which book did you read yesterday?
In this sentence, 'какую' serves as a relative pronoun to refer to a specific road within a context of uncertainty or decision-making. It agrees with 'дорогу' (road) in gender and case.
Она не знала, какую дорогу выбрать.
She didn’t know which road to choose.
Here, 'какую' is used to specify a particular 'идею' (idea) being proposed, linking curiosity with future possibilities.