Questions & Answers about По дороге домой я решил заехать в аптеку за лекарством.
This is a very common Russian expression.
- по дороге literally means along the road / on the way
- домой means homeward / to home
Together, по дороге домой means on the way home.
Russian often uses this kind of compact phrase where English would prefer a fuller expression.
Дороге is in the dative singular.
The preposition по often takes the dative when it means things like:
- along
- according to
- during / in the course of
- in set phrases like on the way
So:
- дорога = road, way
- по дороге = along the road / on the way
This is something learners usually just get used to as a fixed pattern: по дороге + destination.