Quite the mouthful, isn't it? This is a question that will often come up during the "competency" part of the interview, when the interviewer is asking you about your skills and your way of operating. It's usually a fairly easy question to answer, but it will require a bit of thinking on your part.
Why the question is asked
The interviewer is asking you this question to see how you handle situations where you're forced to think beyond the normal day to day tasks. When you're faced with a problem that requires heavy analytical thinking, you're going to have to sit down, evaluate the facts, compile the numbers or data, and come up with a solution based on your analysis. It's much more complex and difficult than the simple problems you face on a daily basis, so it will require more of you as a professional.
When this question is asked, the interviewer wants to see if you can apply your mind to the tough problems and find a solution to them using analytical thinking.
How to answer the question
Before you go into the interview, think about a problem that required a lot of analysis and study to solve.
"When I was in company X, I was given a project that had to be solved within a very short deadline. Management told me it was nearly impossible to finish it within that time frame, but it was something that needed to be done."
Now, think about what you did to solve that problem. Did you just work hard until you got the job done, or did you divvy up the task into chunks so that you could do a bit at a time in order to finish within the deadline? Did you structure the project in order to make it clear what needed to be done and when? Put that into an answer:
"I had to sit down and structure my work in order to meet the deadline. I examined the scope of the project, and determined that I had to do X, X, and X. It required gathering X information, compiling and reviewing X data, and working with X divisions to complete the task."
Now talk about the obstacles you faced. In any tough job, you're going to run into serious snags and setbacks. They are a part of life, and you'll have to deal with them. Show the interviewer that you can analyze the problem, find a solution, and move past the setbacks in order to complete the project within the deadline.
"We ran into X problem, which forced us to reevaluate our way of operating. We had to change X and X, but after we did, we found the project went much more smoothly and we were able to finish on time."
With this question, you're going to have to tell a story, but in a way that shows your skills with critical, analytical thinking and planning. It is a bit tricky so it's worth investing a bit of prep time into crafting a good answer for this question.