This is the 9605th most frequent Russian word.
хмельницком
"Хмельницком" is the prepositional case of "Хмельницкий," referring to the city of Khmelnytskyi in Ukraine.
The word 'Хмельницком' is used here to represent the name of the city 'Khmelnytskyi' in the locative case, indicating the location where the park was opened.
В Хмельницком открыли новый парк.
A new park was opened in Khmelnytskyi.
The word 'Хмельницком' is used here in the locative case to describe the city 'Khmelnytskyi' as the narrator's place of residence.
Я живу в Хмельницком уже пять лет.
I have been living in Khmelnytskyi for five years now.
The word 'Хмельницком' is again applied in the locative case to denote the city 'Khmelnytskyi' as the location frequently visited by the narrator's friends.