"What will you do the day after tomorrow?"
I think it has previously taught us that the other option with 'tien' in was the day before tomorrow?
后天 hòutiān the day after tomorrow 前天 qiántiān the day before yesterday
So, if today is Wednesday (for example) 后天 would be friday and 前天 would be monday.
As you can see, they are much easier to say in Chinese than in English. So, they are much more commonly used in chinese than their English equivalents.
"The day before tomorrow"?!?!???*** That's usually called "today", even in Chinese! ;-)