For most people today multitasking is no longer a nice-to-have skill, but it is a “required” skill. Ultimately however, just a like a computer if you ask it to do more than one thing at a time, your computer tasks will run slower. Your computer’s processor will give a priority to one task at a time and a lower priority to all others.

Our human minds work the same way. If we have 20 things to do and try to do them all at once we will give a priority to one task at any given time (the one we are physically working on) and the others are in the back of our head waiting to be the priority. If we prioritize that second task before completing the first one then the first one we were working on it goes on the backburner while we work on our new priority.

If we continue like this for 20 tasks they may never get done or they will take a considerable amount of time to complete.

When you have 2 or more things to juggle (even 20 things) you must write them down and prioritize them. Your interviewer wants to find out how well you perform when you have multiple things to do. The best approach to this is to explain that you would write down those 20 tasks and you would prioritize the top 3 based on their importance to accomplish. You would also look at the list and note if you “can kill two birds with one stone” with a single task.

Once you have your top 3 tasks you then prioritize those and work fully on the top priority only focusing on the second priority task if priority one is stalled for any reason. Then you would work through the list of 20 like this throughout the day (or days) until all are accomplished with the utmost quality necessary for each task.

If you’d like you may also mention that you would examine your list of tasks a couple times during the day in case you needed to reprioritize based on any new information you obtained throughout the day.

Great answer. The human brain can concentrate on exactly one thing at a time. "Multi-tasking" is actually impossible and "task-switching" is the most accurate term for what many folks do: paying attention to whatever stimulates them at the time (i.e. incoming e-mails, phone calls, a colleague dropping by to ask a question, etc.). Task-switching breaks concentration and reduces efficiency because you are resetting your brain every time you switch. And it is admittedly sometimes a necessary evil in many environments, but many folks let it become the norm unnecessarily.

Most employers will be looking for two things in your answer; an embrace of the fact that we must all manage multiple projects and multiple tasks in parallel, and having a disciplined process/system around which to create efficiency through prioritization and time management.

Assure them that you understand and, perhaps, even enjoy having many things to accomplish. Then let them know how it is that you manage your time and avoid distractions so that you're efficient and effective, especially with regard to important tasks.

I like Covey's 2x2 grid around tasks that are; urgent and important, urgent and not important, not urgent but important (this one still needs attention), and not urgent and not important (round file).

Good answers.
I would also look for the short tasks (hour or less) I can kill quickly, or in-between, to shorten the list faster.