You really need to show more context cuz in my opinion this sentence may come from poet or other literature works...... These days, '고이' is not a popularly used adverb in most situations except for poets. Also this has nuance of one girl (or woman) saying to her invaluable one......

고이: gently with care 접어: conjugation of 접다(fold) indicating successive action. 끌어안는 거: 끌어안다(hold in ones arms; hold something to one's heart) + -는 것 "고이 접어 끌어안는 거 아시죠": = Don't you know I carefully fold it and hold it to my heart? You need more context to know for sure, but it seems to be saying that the speaker is treating something like it is the most precious thing in the world.

means you know, soak it up.