-(으)ㄴ/는 척하다 is attached to a verb, it means ‘to pretend” or “act like(fake)”. For example,
자는 척하지 마. Don’t act like you are sleeping.
너 괜히 아픈 척하는 거지? You are pretending to be sick, right?
다 알면서 모르는 척하고 있어요. (she/he) is pretending not to know, even though (she/he) knows everything.
먹었으면서 안 먹은 척하고 있네. You are acting like you didn’t eat even though you ate.
나 안 좋아하면서 그 동안 좋아하는 척한 거였어? Did you pretend to like me even though you didn’t like me?
곰을 만났을 때 죽은 척하고 있으면 안 돼요. You shouldn’t pretend to be dead when you see a bear.
As you can see, (으)ㄴ 척하다 often comes with (으)면서 because (으)면서 means ‘have two opposite actions/situations at the same time”. If you want to learn more about (으)면서, please click here.