Korean sentence structure is quite different from English. so I arraged it Korean style structure in English. Answer : 나는 과제(숙제)하고 있어요. = 과제하고 있어요 = 프로젝트하고 있어요 나는/ 과제(숙제) / 하고 있어요/ I/ assignment(homework)/ 'm doing 1. 나는 = 'I' We usually skip the subjective like 'I' commonly compared to English. 2. 과제(숙제) = assignment (homework) 과제 means assignment what you have to do like mission. It is commonly used by Univ. Students. 숙제 means homework which can be used when you are child or high schooler. 프로젝트 is just 'project'. You can read it in English. 3. 하고 있어요 = be doing 하고있어요 is basic present progressive form in Korea. For example, If Korean ask you 'Did you get it done?' and you haven't finished yet, You can say 나는 하고 있어요 which has the same meaning as 'I'm doing'. But I said you can skip the subjective , '나는'. So just say 하고 있어요.

Yes