This is the 9466th most frequent Russian word.
узбекистанский
"Uzbekistani" (relating to Uzbekistan or its people).
The adjective 'узбекистанский' is used here to describe the origin of the carpet as being from Uzbekistan.
Я купил узбекистанский ковёр в соседнем магазине.
I bought an Uzbekistani carpet in the nearby store.
The adjective 'узбекистанская' qualifies 'кухня' (cuisine) to indicate that the cuisine pertains to Uzbekistan.
Узбекистанская кухня славится своими национальными блюдами.
Uzbekistani cuisine is famous for its national dishes.
In this sentence, 'узбекистанский' specifies that the art museum is located in or associated with Uzbekistan.