How can an ArcGIS user repair a .mxd file that has broken data sources?

The option to right-click the .mxd file and use the Set Data Sources tool is correct because this tool allows users to directly update the connections to data sources that may be broken or missing. When you have an .mxd file that references data layers which are no longer accessible due to changes in file paths or data location, utilizing this tool provides a simple and effective mechanism to navigate to the current location of your data and re-establish those links.

This option is particularly user-friendly as it can be accessed directly from the file explorer interface, making it straightforward for users to correct issues on-the-fly without needing specialized knowledge of other utilities or tools. By selecting this option, an ArcGIS user can efficiently re-link data sources while working within the familiar ArcGIS environment.

The other options may involve useful tools or functions, but they do not directly address the specific task of repairing broken data sources as effectively as the Set Data Sources tool.