This is the 15980th most frequent Russian word.
прошлогодними
"Last year's" (instrumental plural form).
The word 'прошлогодними' is used as an adjective in instrumental plural form, describing 'воспоминаниями' (memories) with the meaning 'of last year'.
Мы наслаждались прошлогодними воспоминаниями.
We enjoyed last year's memories.
Here, 'прошлогодними' modifies 'усилиями' (efforts) in instrumental plural, indicating that the efforts being discussed pertain to the previous year.
Прошлогодними усилиями удалось достичь больших успехов.
With last year's efforts, we achieved great success.
In this sentence, 'прошлогодними' stands for 'results of last year,' assuming the noun 'результаты,' used in instrumental plural form for comparison.