Being absolutely organized! I work for two busy lawyers and sometimes they run me off my feet, but I keep organized and it keeps me on top of things and in control. When they see me in control they relax and know I will get it done.
You definitely have your hands full. I'm not sure how much work each of these individuals give you, but I am assuming they allocated that many people to one assistant because each person only generates so much work and they assume one person can handle it. I think it would be impossible to work full-time for each of those six people and manage efficiently.
If you do find it overwhelming it may be worth it to speak to your HR manager and see if they can distribute the work more evenly or hire someone to help out.