How do you handle a difference of opinion with your colleagues or superiors? interview question?

Make your case, genuinely listen to their case until you understand it. If you don't understand why they think how they do, keep asking. Look for a compromise or a third way. If it really is one of the two ways, look at the risks and dangers inherent in each. Agree together some kind of scoring system. Work out each position's value. Go with the best position (regardless of who thought of it). Accept the decision and don't take *anything* personally.