Follow these steps to view the Ethernet MAC address of your locally-connected AirPort base station using AirPort Utility 6:

1. Connect to the AirPort base station Wi-Fi network.
2. Open AirPort Utility from the Applications > Utilities folder on your Mac.
3. Select the desired base station by clicking on it once to make the base station edit pop-up appear.
4. Hover the mouse cursor over the light gray name of the base station, located in the top center of the edit pop-up.

The model, Ethernet, and Wi-Fi radio MAC addresses will appear in a base station information pop-up within a few seconds.