It was said on this question in a comment that
조사 "하고(and)" cannot occur together with to 을/를. So if you want to use "하고(and)", it must be "이것하고 저것을 해"
Summarized from a book I have from 연세 University in Seoul, there are 4 ways to use ~고 as a conjunctive ending:
- Two or more sentences are simply listed.
- Two events take place concurrently.
- Two events are in a temporal relationship. THe first event precedes the second.
- Depending upon the verbs used, the first action still continues while the second takes place.
- 새가 울고 꽃이 핍니다 Birds sing (cry), and flowers bloom
- 나는 피아노를 치고 동생은 노래를 불렀습니다 I was playing the piano while my sister sang
- 손을 씻고 저녁 식사를 합니다 (We) wash our hands and eat supper
- 형이 새 옷을 입고 외출했습니다 My brother went out wearing new clothes
From what I'm seeing here, ~고 is a conjunctive ending that fully separates two verbs. How can two verbs separated by ~고 not then also themselves each have their own object to modify with or without 을/를?