This is the 11589th most frequent Russian word.
европейскими
The Russian word "европейскими" means "European" in the instrumental plural form.
The word 'европейскими' here is the instrumental plural form of the adjective 'европейский', describing 'architectural styles' (архитектурными стилями), indicating that these styles pertain to Europe.
Я всегда восхищался европейскими архитектурными стилями.
I have always admired European architectural styles.
The word 'европейскими' functions here as the instrumental plural form of the adjective 'европейский', describing 'traditions' (традициями), showing their connection to European culture.
Он познакомился с европейскими традициями, когда учился за границей.
He became acquainted with European traditions when studying abroad.
In this sentence, 'европейскими' is again the instrumental plural form of 'европейский', modifying 'holidays' (праздниками) to express the concept that these holidays are associated with Europe.