on either hand—
1. on either one of the hands:
- There is no need to move your wedding ring. You can wear an anniversary ring on either hand.
2. positioned to right and left; on both sides:
- See these mountains, standing on either hand, one in the shade and the other in the light.
on every hand—everywhere; on all sides:
- But the retreat was over-hasty, and rich booty remained behind on every hand.