This is the 12852nd most frequent Russian word.
кухне
"Кухне" is the dative or prepositional case form of "кухня," meaning "kitchen" in English.
'кухне' here is used in the prepositional case, denoting the location where the action is taking place.
Она работает на кухне.
She works in the kitchen.
'кухни' here is used in the genitive case, indicating origin or source.
Я принес ей стакан воды из кухни.
I brought her a glass of water from the kitchen.
'кухне' here is used in the prepositional case, specifying the place and emphasizing its condition ('новой' modifies it).