Final answer:
In designing an IPv6 network with both Cisco and non-Cisco routers, the compatible routing protocols are RIPng, OSPFv3, and MP-BGP. RIPv2 and OSPFv2 are only suitable for IPv4 and while EIGRP supports IPv6, it's proprietary to Cisco and may not be compatible with non-Cisco routers.
Step-by-step explanation:
The subject of this question involves the design of an IPv6 network using routing protocols compatible with Cisco and non-Cisco routers. When you're dealing with IPv6, you need to use routing protocols that support this version of the IP protocol. Keeping this in mind, the three routing protocols you can use for an IPv6 network are:
RIPv2 and OSPFv2 are designed for IPv4 and therefore cannot be used in an IPv6 network. Similarly, while EIGRP is a Cisco proprietary protocol that does support IPv6, for a network that uses non-Cisco routers, it's more suitable to stick to open standards which ensure compatibility across different vendors' equipment.