First of all, don't freeze. Survivalist, Bear Grylls has said, "if you do get lost, try to keep calm and come up with a plan." This is what you need to do now. Get your bearings and find a way to move forward. Think about why the interviewer may have asked you this question. Let's assume you are fairly experienced in the field. If the question hasn't come up in your day to day experiences, maybe it indicates some unique aspect of the job you are interviewing for. Remember, the objective of the interview is for the interviewer to discover the things you know and can do for the organization - not what you cannot do.
Likewise, don't ramble. A number of candidates I have interviewed tried to ramble long enough hoping that something he/she said would hit upon the answer I was looking for. Oftentimes, this is very transparent and will likely annoy your interviewer. Also, if you don't know the answer, discussing or describing a different topic will make your interviewer believe you have weak listening skills. No matter how qualified you are, if the interviewer believes you will have difficulty understanding instructions, it may turn off the interviewer regardless of your other great qualities.
Don't get flustered. There's no need to shut down or get defensive. Everything you said about how you are a great team player and handle pressure like a pro is on showcase now. Your interviewer is using these questions to genuinely discover whether you have the qualities and skills needed at the organization. Unfortunately, most interviewers are not adequately trained to do this effectively. That's why it's up to you to keep calm and help your interviewer with this objective.
So, when encountering a interview question you don't know the answer to, consider the following steps and how to apply them to your situation:
1) Keep calm. This is very important. I know it's easy to say but hard to do. Fortunately, with practice, this becomes easier.
2) Think about why the interviewer asked this question. The irony is that an interview session can reveal a lot more about the interviewer than interviewee just by examining the questions that were and were not asked.
3) If applicable, ask some clarifying questions. Try to use examples that help both of you get on the same page. You would be surprised how often the question the interviewer had in mind is not the same as what the interviewee understood.
4) If this is a problem solving question, break the problem down to smaller problems. Discuss your approach and make abundant use of diagrams. Treat the situation as a collaborative problem-solving session with the interviewer. If, at the end, you are unable to solve the problem, the interviewer has a practical understanding of how you approach issues and collaboration with others. These qualities speak volumes to interviewers who know how to build healthy organizations.
5) If this is a knowledge question, be willing to admit you do not know the answer. Approach the situation with a healthy curiosity. Is the knowledge represented by the question representative of the work the role requires? Are there experiences you have had in the past that are similar or allow you to adapt quickly? This is your opportunity to explore that.
Let us know about interview questions that stumped you and how you overcame your challenge.