In this question the interviewer is trying to test your knowledge of the many industry standard methodologies and their advantages & disadvantages, and whether you’re able to apply the right methodology for the given project.
The best way to answer it is to pick two opposing methodologies which you’ve used when delivering a project. Then state a positive attribute of both methodologies whilst placing a greater positive emphasis on the favourite methodology of the two.
For example for a project manager delivering an IT project a good answer could be:
I like the structured approach and the sense of control I get with the waterfall methodology, however in this industry changes to the specification are sudden so an iterative methodology like Agile is my favourite for technology projects.