How to use a multimeter to check R, C, W, and Y terminals if the thermostat is wired incorrectly

During the commissioning of a small commercial project, when the thermostat is set to cooling, the fan starts but the outdoor unit does not respond. Someone on-site wanted to replace the thermostat directly, but I usually check the wiring first, as incorrect connections at the R, C, W, and Y terminals are very common. My procedure is to first cut the power and take a photo to confirm the…