This is the 9393rd most frequent Russian word.
тихвинского
"Of or related to Tikhvin," a town in Russia.
In this sentence, "тихвинского" is used as a genitive case of an adjective modifying "монастыра," referring to the possession or association with Tikhvin.
Я посетил тихвинского монастыра в этом месяце.
I visited the Tikhvin monastery this month.
Here, "тихвинским" functions as an instrumental case of an adjective describing "окружением," indicating the quality related to Tikhvin.
Мы познакомились с тихвинским окружением в процессе исследования.
We became familiar with the Tikhvin environment during the investigation.
In this instance, "тихвинскому" is in the dative case of the adjective modifying "музею," showing the relation or reference to Tikhvin.