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Don't take your eyes off your bag while walking.
Literal
Walking-during [at-に] bag [from-から] eyes [obj-を] don't-release [so that-ように].
Two useful pieces. 歩行中 ('during walking') uses the suffix 中 ('in the middle of, during'); 会議中 ('during a meeting'), 食事中 ('during a meal'). 目を離す ('take one's eyes off') is a body-action idiom literally 'release the eyes.' The trailing ~ように without a main verb is an admonition or instruction, common in warnings: 'be sure (not) to do X.'