This question is one reason to do some research on the organization before the interview. Find out where they have been and where they are going. What are the current issues and who are the major players?
This may take some thought and certainly, should be based on the research you have done on the organization. Sincerity is extremely important here and will easily be sensed. Relate it to your long-term career goals.
You should be clear on this with your family prior to the interview if you think there is a chance it may come up. Do not say yes just to get the job if the real answer is no. This can create a lot of problems later on in your career. Be honest at this point and save yourself future grief.
The interviewer is not looking for a long or flowery dissertation here. Do you have strong feelings that the job gets done? Yes. That's the type of answer that works best here. Short and positive, showing a benefit to the organization.
You are, of course, a team player. Be sure to have examples ready. Specifics that show you often perform for the good of the team rather than for yourself are good evidence of your team attitude. Do not brag, just say it in a matter-of-fact tone. This is a key point.
This is serious. Do not make light of it or in any way seem like you like to fire people. At the same time, you will do it when it is the right thing to do. When it comes to the organization versus the individual who has created a harmful situation, you will protect the organization. Remember firing is not the same as layoff or reduction in force.
A loaded question. A nasty little game that you will probably lose if you answer first. So, do not answer it. Instead, say something like, That's a tough question. Can you tell me the range for this position? In most cases, the interviewer, taken off guard, will tell you. If not, say that it can depend on the details of the job. Then give a wide range.
Specifics here are not good. Something like this should work: I'd like it to be a long time. Or As long as we both feel I'm doing a good job.
Try to avoid labels. Some of the more common labels, like progressive, salesman or consensus, can have several meanings or descriptions depending on which management expert you listen to. The situational style is safe, because it says you will manage according to the situation, instead of one size fits all.
Several ways are good measures: You set high standards for yourself and meet them. Your outcomes are a success. Your boss tell you that you are successful.