There is a method to buy time to think of your answer by asking the other person to answer first. Even if you don't know the answer right away, having a bit of time might help you come up with a response. While the other person is answering, take the opportunity to formulate your thoughts. Additionally, by asking the other person to answer first, you can say, "I was thinking the same thing," when it's your turn. However, this tactic can be considered a bit sneaky, so it's not highly recommended.
For example, if you are asked, "What is your biggest failure?" you could respond with, "Are you asking about work or personal life?" or "It depends on how you define failure." This way, you can buy a bit of time to think and increase your chances of giving the best possible answer on the spot.