Double Star Thru is a regular Star Thru followed by a reverseStar Thru. For the second one, the boys will be using left hands and turning left, while the girls will be using right hands and turning right. The girl still passes under the arch.
Triple Star Thru adds another regular Star Thru, so that for the boys the sequence will be right-left-right, and for the girls the sequence will be left-right-left. In most cases not all the dancers will be doing all the parts.