When you add 놓다, 두다 to verbs, it adds the meaning that you are doing it in advance for something else, or for later. 'verb + 놓다' is used a bit more often than '두다' but you can use them interchangeably in most cases. They do not have much difference in terms of meanings. However, here are some differences in usage. 1.'놓다' can be used with negative meanings of verbs but '두다' cannot be use with them. e.g. 제 동생이 제가 만든 케이크를 망쳐 놓았어요. (O) 제 동생이 제가 만든 케이크를 망쳐 두었어요. (X) 2. '놓다' can be used with adjectives but '두다' can't. e.g. 저 옷은 너무 비싸놓아서 아무도 안 사요. (O) 저 옷은 너무 비싸두어서 아무도 안 사요. (X)