Answer: Tuesday, July 9 (correct me if I'm wrong)
Step-by-step explanation:
Jen goes every other day, so she goes every odd day.
Terry goes every third day, so Jen and Terry go together every six days.
Six days later is Sunday June 9, then Saturday June 15, then Friday Jun 21, then Thursday June 27, then Wednesday July 3.
Carlos only comes Mondays and Tuesday, so the next six days would be Tuesday July 9.