This is the 12491st most frequent Korean word.
닿게
"닿게" means "to touch" or "reach" in a certain way.
In this sentence, '닿게' indicates the proximity needed between the hand and the wall to facilitate contact.
손이 닿게 벽에 가까이 다가가세요.
Move closer to the wall until your hand touches it.
Here, '닿게' describes the manner in which his words impact or reach one's heart, metaphorically.
그의 말이 마음에 닿게 들렸습니다.
His words sounded touching in my heart.
In this case, '닿게' illustrates the action of sunlight reaching and contacting the leaves.