'떡이 지다' or '떡 지다' means 'stringy', 'oily' or 'greasy' when you use it about someone's hair. - 이틀 동안 머리를 감지 않아 머리가 떡 졌어요. (My hair got stringy as I didn't washed my hair for 2 days.) Also, '떡 지다' means that something is 'sticky', especially about Korean rice that cooked with too much water so it became like a glue stick. - 밥이 떡 져서 먹기 싫어요. (I don't want to eat this rice as it is too sticky.) I hope it can help you. :) + Plus I wrote it with a space like '떡 지다', many people use just without the space like '떡지다'. If someone want to find some sentences on internet, then it's better to serch without the space.