This is the 7206th most frequent Russian word.
великолукской
"Of or related to Velikiye Luki," a city in Russia.
Here, 'великолукской' is used as an adjective derived from 'Великие Луки,' referring to something related to this locality, specifically the youth.
Я часто слышу истории об интересной жизни великолукской молодежи.
I often hear stories about the interesting life of young people from Velikiye Luki.
Here, 'великолукской' modifies 'администрации' (administration), denoting affiliation with the location Velikiye Luki.
Новый проект великолукской администрации вызвал много вопросов.
The new project of the administration of Velikiye Luki raised many questions.
In this context, 'великолукской' describes 'истории' (history) showcasing it is related to Velikiye Luki.