This is the 9847th most frequent Russian word.
австрийских
"Австрийских" means "Austrian" in English (genitive plural or genitive singular feminine/neuter form).
Here, "австрийских" is used as a plural form of the adjective "австрийский" (Austrian), agreeing with plural noun "композиторов" (composers).
Я люблю австрийских композиторов, как Моцарт.
I love Austrian composers like Mozart.
"Австрийских" functions here as an adjective describing "традициях" (traditions) in plural form, emphasizing origin or association.
Вчера мы смотрели фильм об австрийских традициях.
Yesterday we watched a movie about Austrian traditions.
In this case, "австрийских" is used as an attribute for "художников" (artists), also in plural, indicating the nationality or origin of the painters.