This is the 9675th most frequent Russian word.
черкасской
"Черкасской" means "of Cherkassk" or "related to Cherkassk," referring to the town or region.
In this sentence, 'Черкасской' is used in the genitive case to describe the location or attribute of the art museum.
Она посещала Черкасской художественный музей.
She visited the Cherkassy Art Museum.
Here, 'Черкасской' is used in the genitive case to indicate the region related to history.
Он интересуется историей Черкасской области.
He is interested in the history of the Cherkassy region.
In this sentence, 'Черкасской' modifies 'культуре' to denote a cultural aspect tied to Cherkassy.