The two words are not synonyms.
* 포개다 = 1) stack things on top of one another, 2) fold together (=개다). (the point is to take up less space)
* 가리다 = cover something to conceal it from view. (the point is to keep it out of sight)
(가리다 has another unrelated meaning "to choose, screen, differentiate", e.g. 이 경기에서 우승자를 가린다 (We'll select the final winner in this game).
* 이불을 한 구석에 포개어 놓았다 = I folded the blanket neatly in one corner.
* 그녀는 입을 가리며 웃었다 = She laughed covering her mouth.
* 앞 사람이 시야를 가렸다 = The person before me blocked my view (시야 = (field of) view).