Which situation would require a vehicle to have its brakes checked?

The correct choice indicates that any failure in brake function would necessitate having the brakes checked. This is crucial because brakes are critical components of vehicle safety. If there is any indication that the brakes are not functioning properly—such as unusual sounds, a soft brake pedal, or decreased stopping power—it's imperative for the driver to investigate further. This could help prevent serious accidents caused by brake failure, which can lead to loss of control over the vehicle.

Other situations mentioned, such as the vehicle not starting or displaying a Red R sticker, do not inherently relate to the need to check the brakes specifically. Hitting a pothole might potentially cause damage that could impact brake performance, but it does not automatically require an inspection unless there are indicators of brake issues. Therefore, the most comprehensive and immediate trigger for checking brakes is any failure in their function.