This question is quite an easy one, but it is important not to fall into the trap of giving a general answer instead of a specific one. The question has asked you to describe a time, not a circumstance that you regularly find yourself in.
Try to think of a specific occasion when you have had to deal with a number of conflicting demands on your time, which for most people would be every hour of every working day, and give a specific example as to how you dealt with it. It is not really a competency based interview question but more of one requiring you to give a specific example backed up with evidence as to how you handle such a situation.
Be very careful not to give any negatives in this answer. It is important to make sure any answer is positive and has no negative connotations.
Examples of Answers
“Whilst working as area manager for Boots one of my colleagues covering a number of stores in the next sector was suddenly taken ill in the run up to an important conference where they were expected to present their findings on a study recently undertaken in their area.
Senior management felt that an interim manager would not be able to handle the level of intensity of the post and I was asked to take over the presentation of the findings as well as manage my own area and my colleagues. In order to do this I immediately delegated all non-essential or urgent tasks to members of my team after holding a meeting to determine how we could do this, and concentrated on the main actions required which included the presentation.
The outcome of this decision was that the presentation went ahead smoothly, my colleagues and I experienced an increased workload but as a result of my decision to delegate all tasks were completed within time and on budget.