챙기다 is making sure something actually gets done or brought along — 잊지 않고 챙기다, not forgetting the coupon or the school bag, which two captions here use. Aimed at a person it means looking after them: noticing what they need before they say it, making sure they eat. 챙겨 주다 is doing it for someone else, and in two lines it sits alongside the words for cherishing and caring for.