Final answer:
A device learns its IPv6 subnet prefix via router advertisements as part of the Neighbor Discovery Protocol, allowing for automatic network configuration without manual settings or extensive server support.
Step-by-step explanation:
The device learns the value of the IPv6 prefix for its subnet through router advertisements. When a device is configured to use IPv6 and connected to a network, it sends out a request upon joining the network. The local routers respond with router advertisement messages that contain network layer configuration parameters, including the IPv6 prefix used in the subnet. This process is part of the Neighbor Discovery Protocol (NDP), which is designed to operate without the need for manual configuration and with minimal support from network configuration servers.