This is the 6191st most frequent Polish word.
bachmutem
"Bachmutem" is the instrumental case of "Bachmut," the Polish name for Bakhmut, a city in Ukraine.
Here, 'Bachmutem' is used as a proper noun indicating the place name 'Bachmut', in instrumental case form, following the preposition 'przez' to describe the action of traveling through this place.
Podróżowaliśmy przez Bachmutem, aby zobaczyć jego zabytki.
We traveled through Bachmutem to see its monuments.
In this sentence, 'Bachmutem' is used in instrumental case to complement its relationship to 'miasta', describing its name in the context of possession or locality.
Rozmawiałem z mieszkańcem miasta Bachmutem o jego historii.
I spoke to a resident of the city of Bachmut about its history.
Here, 'Bachmutem' is part of the description showing location and importance, instrumental case despite 'do' which normally requires genitive, usage suggesting stylized or regional speech forms.