This is the 768th most frequent Turkish word.
düzce
Düzce: A city and province in northwestern Turkey.
Here, 'Düzce' is a proper noun referring to a city in Turkey, used as the subject of the sentence.
Düzce çok güzel bir şehir.
Düzce is a very beautiful city.
In this usage, 'düzce' functions as an adverb, implying walking straightly without deviation.
Yolda düzce yürümeye çalış.
Try to walk straight on the road.
Here, 'düzce' is used as an adverb to describe the manner of spreading the carpet smoothly or evenly.