This is the 13224th most frequent Russian word.
многолетнюю
"Многолетнюю" means "perennial" or "long-term" in English.
In this sentence, 'многолетнюю' is used as an adjective in accusative case, qualifying 'проектом', indicating that the project spans several years.
Она занимается многолетнюю проектом по сохранению лесов.
She is engaged in a years-long project to conserve forests.
Here, 'многолетнюю' is an adjective in the accusative case, describing 'дружбу', highlighting the long duration of the friendship.
Его многолетнюю дружбу с соседями нельзя недооценивать.
His many years of friendship with his neighbors cannot be underestimated.
In this usage, 'многолетнюю' modifies 'карьеру' in the accusative case, emphasizing the longevity of the career.