On either or both sides. It was quite breathtaking walking at the very bottom of the Grand Canyon, with colossal, ancient cliff faces towering over you on either hand.He strolled into the room with a beautiful woman on either hand.See also: either, hand, on
on either/every ˈhand
(literary) on both/all sides; in every direction: We were surrounded on every hand by dancing couples.See also: either, every, hand, on