This is the 8932nd most frequent Russian word.
пушкинский
"Pushkinsky" refers to something related to Alexander Pushkin, a famous Russian poet and writer.
In this sentence, 'пушкинскую' describes 'поэму' (poem), indicating that the poem is related to or authored by Pushkin.
Я прочитал пушкинскую поэму вчера.
I read a Pushkin's poem yesterday.
Here, 'пушкинском' refers to the style of the artworks, implying features reminiscent of Pushkin's era or influence.
На выставке представлены картины в пушкинском стиле.
At the exhibition, there are paintings presented in the Pushkin style.
In this example, 'пушкинских' modifies 'мест' (places) to denote locations associated with Pushkin.