Saturday.
Friday
Today is Sunday. Monday is the day before two days after today (the day before tomorrow). Monday is the day before Tuesday. Two days after today is Tuesday.
Sunday
To solve the riddle, we start from "the day after the day after tomorrow," which is two days from today. If that day is four days before Monday, then two days from today is Sunday (since four days before Monday is Thursday). Therefore, today is Friday.
4
The day must be Thursday because "the day after tomorrow" means two days into the future and two days before Sunday is Friday. that means that yesterday would have been Thursday.
Sunday
The day before today. Two days before tomorrow. But if tomorrow never comes, will yesterday ever go. =/ At the time of this writing, yesterday was Sunday, January 1st, 2011.
Saturday
Sunday Day before yesterday = Wednesday Yesterday = Thursday Today = Friday Tomorrow = Saturday Day after Tomorrow = Sunday
Tuesday
If 4 days after the day before yesterday is Sunday tomorrow is... 7-4+2+1 = 6 (Saturday) Forget the first part. Tomorrow is Tuesday. Great question.