The top skills required in convincing your manager are communication and strong persuasion. You must get everyone on board if your approach aims to provide a better result. The interviewer asks this question to determine if you can influence people positively and anticipate good outcomes. It would help if you did not sound over-confident while responding. Having patience is a crucial factor; make sure to include it in the answer. Give specific details to make it sound crisp. Try using some stats, and your outcome must reflect the beneficial nature of your persuasion. Even though your persuasion was for good, do not come off as someone who is not flexible and opposes others' ideas. Maintain transparency throughout. Your approach must be divided into parts showing the plan you made, which must include your ideas & why they can be beneficial before approaching your head. Prepare a detailed analysis of how your strategy will work and the risks involved. Offer the solutions to the problems with great surety in yourself. Do not risk being looked at as pushy. Include examples and show enthusiasm. Another important aspect will be to handle objections. Frame your answer around these aspects and use some instances to support your ideas.