With multi-tasks going on simultaneously, you need to prioritize the tasks in terms of timeline and importance, so that time and resources would be managed effectively. You need to plan ahead, and set up several milestones along the schedule, so that you would be able to follow up and follow through.
2. Be result-oriented.
No matter how many tasks you are managing at same time, once you promise, you need to deliver the results. And no matter how well you planed, execution and implementation are the key to make things happen.
3. Meet the timeline and keep related parties informed about the status.
You need to deliver the results within the timeline. However, along the way, you need to constantly keep all the related parties (e.g. your boss, teammates, or other departments) informed what is going on. In case that anything unexpected happens, no one would have a last-minute notice or last-minute surprise. (Personally, I hate a last-minute surprise the most.)
The above is just what I would answer. I suggest you to look at your own experience and find an adequate example so that the key points would be presented perfectly.