This is the 7614th most frequent Russian word.
екатерининском
"Екатерининском" is the prepositional case of an adjective meaning "of or related to Catherine" (often referring to Empress Catherine or something named after her).
Here, 'Екатерининском' is used to describe 'сад', showing possession or naming it 'Catherine's Garden'.
Мы гуляли по Екатерининском саду в парке.
We walked in the Catherine's Garden in the park.
In this example, 'Екатерининском' modifies 'дворце', referring to the 'Catherine Palace.'
В Екатерининском дворце проходило торжественное мероприятие.
A ceremonial event was held in the Catherine Palace.
'Екатерининском' here characterizes 'мосту,' naming it as 'Catherine’s Bridge.'