The root of "한눈을 팔 것" would be "한눈팔다". The meaning of "한눈팔다" is "someone has to focus on something important, but he/she doesn't". For example, "아들아, 학교가 끝나면, 한눈팔지 말고 곧장 집으로 와라" = "Son, come home right after the school. Don't go any other places" "그는 일에 집중하지 못하고 계속 한눈을 팔고 있었다." = "While he was working, he couldn't concentrate on his work. He was distracted". FYI, 한눈팔다 = 한 + 눈 + 팔다, where "한" is "one", "눈" is "eye", and "팔다" is "to distract".

한눈을 팔다. means be not concentrating something. So if it says 한눈 팔지마세요. Means don't lose your concentration. If Girlfriend tell boyfriend '다른 여자에게 한눈팔지마.' Means don't look at another girl. Only look at me. I hope you understand it