Demonstrate empathy, data-backed communication, and a win-win outcome.
How to answer it
A conflict story needs two reasonable people who wanted different things. If the stakeholder was simply wrong, it is not a conflict and the interviewer learns nothing about you.
Structure:
The disagreement, fairly stated from both sides. "Marketing wanted attribution to credit the last touch, because that is what their spend decisions run on. I wanted multi-touch, because last-touch was giving all the credit to branded search, which people only type after seeing an ad."
What you did first. Listened, and worked out what they actually needed: not a particular model, but numbers they could act on weekly without relitigating the methodology.
The move that resolved it. "I proposed reporting both, side by side, for one quarter, with a note on where they disagreed. Where they agreed, no one had to argue; where they disagreed, we had a specific campaign to look at instead of a general debate."
The outcome. "After a quarter they asked to switch the primary view to multi-touch themselves, because the disagreements had all gone the same direction."
What to make visible: you separated the person from the position, you found the underlying need, and you chose a resolution that let the data settle it rather than a meeting.
What they are checking: whether you can state the other side's case as well as your own, and whether the resolution was a decision or just an accommodation.
Common mistake: a story where "resolved" means you escalated and won.