This is the 13703rd most frequent Polish word.
podkarpackiego
"Podkarpackiego" refers to something related to the Podkarpackie region (Subcarpathian Voivodeship) in Poland.
Here, 'Podkarpackiego' functions as a noun form, used to indicate the region (Podkarpackie) as the origin of someone.
Spotkałem podróżnika z Podkarpackiego.
I met a traveler from the Podkarpackie region.
Here, 'podkarpackim' is used as an adjective describing the voivodeship (region) specifically.
Mieszkam w województwie podkarpackim.
I live in the Podkarpackie voivodeship.
In this sentence, 'podkarpackiego' is an adjective associated with the noun 'lasu' (forest), modifying it by specifying its relation to Podkarpackie.