Answer:
its Wednesday
Step-by-step explanation:
Tracy thinks its Monday
Melissa thinks its Saturday
Ben thinks its Thursday
Adrienne thinks its Saturday
Suzie thinks its Friday
Darryl thinks it's either Sunday, Monday, Tuesday or Wednesday
David thinks its either Monday, Tuesday, Thursday, Friday, Saturday or Sunday.
Three people think its Saturday so that option is ruled out since they can't all be right
Monday is also ruled out because if its Monday, that means Tracy, David and Darryl are right and that can't happen
Thursday is ruled out because if it is Thursday, both David and Ben are right and that can't happen
Friday is ruled out because Suzie and David can't both be right
Tuesday is out because both Darryl and David think it could be Tuesday
Sunday is also out because Darryl and David think it could be Sunday
That leaves Wednesday and that is the day of the week since only one person's statement (Darryl's) was right.