In IPv6, addresses are categorized into various types including link-local, global unicast, multicast, and loopback. Link-local addresses (beginning with fe80) are used for communication within a single subnet and can be configured on router interfaces. Global unicast addresses (beginning with 2001) are routable on the internet and also can be configured on router interfaces. Multicast addresses (beginning with ff00) are used to deliver packets to multiple hosts and are not assigned to interfaces, while the loopback address (::1/128) is used for internal testing. Therefore, the valid options for configuration on a router's interface are fe80:13dc::1/64 and 2001:12e3:1b02::21/64.