This is the 13014th most frequent Russian word.
льняных
"Льняных" means "linen" or "made of linen" in English.
The word "льняных" is used as an adjective, describing the material composition (linen) of the shirts.
Я купил льняных рубашек на лето.
I bought linen shirts for summer.
Here, "льняных" serves as an adjective modifying "ниток" (threads), indicating that the threads are made of linen.
Льняных ниток не хватило для вышивки.
We ran out of linen threads for embroidery.
In this case, "льняных" describes "фабрик" (factories), specifying that these factories mainly produce linen-based products.