-아/-어 내다 is a fairly simple grammatical principle that packs a lot of meaning. Like many grammatical principles in Korean, it creates a nuance rather than changing the basic meaning of a sentence. Unlike some of the other principles though, this one is usually easily translatable to English.
When you add this principle to a verb it changes the sentence from “I did X” to “I managed to do X” or “I managed to get X done”. The included meaning is that accomplishing X required the subject of the sentence to put in great effort and/or endure hardship.
-아 내다 / -어 내다 can only be added to verbs, not adjectives. Attach it by following the rules found in this lesson. Because of it’s meaning, -아/-어 내다 is almost exclusively used in the past tense, so it must be conjugated according to the rules found in this lesson.
We are Bulletproof: the Eternal:
다 호기롭게 우린 막아냈지 ~ “Bravely we managed to fend them all off.”
Original verb: 막다 – to block, to fend off
날 찾아냈잖아 날 알아줬잖아. ~ “You managed to find me. You understood me.”
Original verb: 찾다 – to find
등골브레이커 (Spine Breaker):
떼를 쓰고 애를 써서 얻어냈지. ~ “You managed to get [your padded jacket] because you whined and pestered.”
Original verb: 얻다 – to get, to obtain
너의 마음은 마치 단두대처럼 나를 싹둑 가차없이 잘라냈지만 ~ “Like a guillotine, your heart [managed to] mercilessly cut through me with a swish, but…”
Original verb: 자르다 – to cut, to sever