This is the 2772nd most frequent Russian word.
мелитопольском
"Мелитопольском" refers to something related to Melitopol, a city in Ukraine.
In this sentence, "мелитопольском" is used as an adjective describing the region ('районе'), indicating its connection to Melitopol.
Я вырос в Мелитопольском районе, который славится прекрасными садами.
I grew up in the Melitopol region, which is famous for its beautiful gardens.
Here, "мелитопольском" modifies the noun 'вокзале' (train station), specifying its location as in Melitopol.
На мелитопольском вокзале всегда много путешественников.
There are always many travelers at the Melitopol train station.
The word "мелитопольском" in this sentence is an adjective describing the institute ('институте'), showing its affiliation to Melitopol.