"We are sleeping for six days."
Translation:우리는 엿새 동안 자요.
일 is a bound noun, so it is 육 일. While you're somewhat right, they are still used not too rarely. I think a few young Koreans confuse 사흘 with 사 일 because it's both 사, you know, and then they are like "If 사흘 is four days, what is 나흘?" Not to offend anyone, but nevertheless you'd look very uneducated if you didn't know those words (as a native speaker).