There are at least threefive options available to the ISP for doing this.
- Assign you a private V4 IP and run a conventional V4 NAT at the ISP level.
- Use "ds-lite" which tunnels IPv4 packets over IPv6 to a special NAT at the ISP.
- Use "464XLAT" where your router performs a stateless NAT46 and then the ISP performs stateful NAT64.
- Use "map-e", in this system each client is assigned an IP address with a restricted set of ports. The client's router performs NAT using the restricted port set and then tunnels the packets over IPv6 to a special device at the ISP. Traffic returning to the client is encapsulated in IPv6 and then sent to the relavent client based on IP and port.
- Use "map-t", similar to MAP-e the client gets a restricted port set, but rather than being encapsulated the traffic is translated to IPv6 for it's journey over the ISPs access network.
Your router may need replacement or a firmware upgrade to support the latter four options.
The advantage of the latter two options is that the ISPs equipment is "mostly stateless", meaning that asymmetric routing and re-routes won't break things.