Where does “autókölcsönzők” come from?

autókölcsönzők (Hungarian) comes from Hungarian autókölcsönző, from Hungarian autó, from German Auto, from German automobil, from Spanish automóvil, from Russian автомоби́ль, from French automobile, from French auto- — Postpositional intensifying particle: indeed, at any rate, in fact.

Ancestry of “autókölcsönzők”, step by step

Step	Language	Word	Meaning
1	Hungarian	autókölcsönző	rent-a-car; car rental agency
2	Hungarian	autó	auto, automobile, car
3	German	Auto	car
4	German	automobil	automobile
5	Spanish	automóvil	automobile
6	Russian	автомоби́ль	car, automobile, motorcar
7	French	automobile	automotive; automobile
8	French	auto-	auto- regarding oneself
9	Ancient Greek	αὐτο-	self-
10	Ancient Greek	αὐτός	αὐτή f, αὐτό n; "first/second declension";...
11	Proto-Indo-European	h₂ew	away from, off; again
12	Proto-Indo-European	ǵʰe	Postpositional intensifying particle: indeed, at any rate, in fact

Every word from Proto-Indo-European ǵʰe →Every word from Proto-Indo-European h₂ew →Every word from Ancient Greek αὐτός →