Let's face it: you want to nail your interview. Instead of answering an interview question about a challenge or problem you have overcome, your interviewer might turn the tables on you. Be prepared to discuss the biggest challenge you will potentially face in the new position. A strong response will show your future employer how well you've matched yourself to the job posting.
One of the ways you can answer this interview question is to focus on your flexibility. You don't have to describe how you overcame a past challenge, but do discuss how previous jobs helped you become very flexible. For instance, you can explain how you will address an assignment that you're given at the last minute and still do your best.
Flexibility goes well with responsiveness. Whatever the demands of a new position will be, you've got to convince the interviewer you can meet them. Pick one issue that might arise in this position and offer a short description of how you would respond. Be careful not to give an answer that portrays you as a reactive person. For instance, a manager must give an appropriate and helpful response to an escalating situation, such as a customer getting very loud and abusive towards a worker.
An important quality to some workplaces is how you might blend in with the work culture. Demonstrate this quality even when you're not sure what that involves. For instance, you could talk about how your biggest challenge is to switch your management style to a new company's system of management. Your interviewer may zoom in on this remark, and so you must prepare to discuss the differences between what you've done and what you will do.
The interviewer wants to know whether you will stay on in the job and be content. Describe your biggest challenge as learning a new position and preparing yourself to handle the many career opportunities the new organization offers. Focus on how you want to develop as a professional without sounding as if you would leave if you found a better job.