This is the 3871st most frequent Polish word.
prezydenckim
"Prezydenckim" means "presidential" in English.
Here, 'prezydenckim' is used as an adjective to describe the type of palace, specifically a 'presidential' palace.
Andrzej mieszka w pałacu prezydenckim.
Andrzej lives in the presidential palace.
The word 'prezydenckim' describes the car as being related to a president, indicating that it is used by or designated for a president.
To jest samochód prezydencki.
This is the presidential car.
In this case, 'prezydenckim' is metaphorically indicating a style or manner associated with or characteristic of a president.