This is the 7553rd most frequent Russian word.
донецкую
"Донецкую" is the accusative singular feminine form of "Донецкий," meaning "Donetsk" (related to Donetsk, a city or region in Ukraine).
Here, 'донецкую' functions as an adjective describing the noun 'газету,' referring to something associated with Donetsk City.
Он купил донецкую газету.
He bought a Donetsk newspaper.
In this sentence, 'донецкую' modifies the noun 'фабрику,' indicating that the factory is located in or related to Donetsk.
Мы посетили донецкую фабрику.
We visited the Donetsk factory.
Here, 'донецкую' is used adjectivally to qualify 'культуру,' meaning the cultural aspects associated with Donetsk.