Katniss and Peeta are liars. They both lie on some specific days.
Katniss lies of Fridays, Saturdays and Sundays. She speaks truth on all other days.
Peeta lies on Tuesdays, Wednesdays and Thursdays. He speaks truth on all other days.
Can you tell that one day of the week when both of them will say "Tomorrow, I will lie."?
Suppose that the person is speaking truth, he/she will have to lie on the next day but if he/she speaks lie by saying "Tomorrow I will lie.", then he/she will have to speak truth on the next day.
Thus, in each of the case, they will have to change their behavior the next day.
Now if you analyze, you will find out that Katniss can only say that statement on Thursday or Sunday. Peeta can say that statement on Monday or Thursday. Thus the only day common is Thursday.