This is the 4664th most frequent Russian word.
дорогами
"By roads" or "through roads."
In this sentence, 'дорогами' ('roads') is used in the instrumental plural case to describe the paths traveled.
Мы путешествовали по старым дорогами страны.
We traveled the old roads of the country.
Here, 'дорогами' illustrates reflection and nostalgia, referencing metaphorical paths representing stages of life.
Он всегда мечтал пройтись дорогами своего детства.
He always dreamed of walking the roads of his childhood.
In this example, 'дорогами' emphasizes the environment through which an action occurs.