What do you do when an E6 tasks people who aren't in his platoon, and you (an E4) suffer for their incomplete tasking?

You need to talk to your first line supervisor. In the Army I wouldn't allow another E6 to just start tasking out my Soldiers without first consulting me. However, at the end of the day you need to do what you're told until you can rectify the situation.

This happened when 3 of my soldiers and myself were medical support for a BWC. We had lanes to run and someone came over a tasked my soldiers with "move this over there and that over here" type of nonsense because he wanted to be done faster. They completed the tasks but then came and found me. I spoke with the other NCO and stated that IF we had down time from our tasks, I would send support to him to help out, however at the moment we were tasked with our own mission and to please speak with me prior so that I may maintain accountability of my guys at all times. I do like to maintain that level of respect, but I also will not let my soldiers be taken advantage of. If he were to try and discipline them, however that would be another story. Unless you are their first sergeant, commander, or platoon daddy than I want to know what they are being disciplined for and I want to be present when said conversation takes place.

I know as a squad and acting platoon sgt at Ft. Hood, I would be pissed if someone tasked my guys out without coming to me first.