This is the 11476th most frequent Russian word.
долгого
The Russian word "долгого" means "long" or "lasting" (genitive or accusative singular masculine/neuter form).
Долгого is in the genitive case to agree with пути, showing possession or relation and the word means 'long' here.
Он прошел долгого пути, чтобы достичь этой цели.
He has traveled a long way to reach this goal.
Долгого is in the genitive case due to the preposition после, describing the duration of the day.
После долгого дня прогулок, я чувствую себя усталым.
After a long day of walking, I feel tired.
Долгого is in the genitive case to agree with разговора and illustrates the idea of extensive length in time.