This is the 9785th most frequent Russian word.
эту
"Эту" means "this" (feminine, accusative case) in English.
Here, 'эту' (this) is used as a demonstrative pronoun modifying the noun 'книгу' (book) in the accusative case.
Я взял эту книгу с полки.
I took this book from the shelf.
'эту' acts as a demonstrative pronoun before the noun 'девушку' (girl), again in the accusative case, indicating a particular object.
Ты видел эту девушку вчера?
Did you see this girl yesterday?
'эту' serves as a demonstrative pronoun modifying 'проблему' (problem), showing specificity in accusative singular form.