게 땡기다

pull hard or taut (casual spelling)

땡기다 is how people say and write 당기다 'pull' in relaxed speech; you would not use this spelling anywhere formal. The adverbs before it here are either force words — 세게, 팽팽하게, 엄청나게 — or the pointing words 이렇게 and 그렇게, spoken while showing the action. So the phrase is about pulling something hard or tight: 얼굴을 팽팽하게 땡겨주면 'if you pull the face taut', 턱을 좀 이렇게 땡겨서 'tuck your chin in like this'.

Register: casual, non-standard spelling