It's pretty simple. If IPv6 headers were split into two parts, where the first part was the same as IPv4, and the second part had the rest of the bits, so you had say 8 octets instead of 4. The rest of the header would look like data to an IPv4 router.

So your IPv6 address would be 1.2.3.4.5.6.7.8. The header would have 5.6.7.8 as the IPv4 destination. When it got there, that router would unpack the rest of it and send it off to 1.2.3.4.5.6.7.8. If that host had to talk to an IPv4 host, it would just use the IPv4 headers.

Then IPv6 traffic could pass over IPv4 networks without any changes. The only constraint would be that each IPv6 network would have to have an IPv4 "gateway" address.

Old IPv4 hosts wouldn't be able to talk to IPv6 endpoints, but at least this way the user could upgrade their own stack without having to wait for their ISP, and every network in between, to also upgrade.

It's pretty much carrier grade NAT but from client to client without ISP support being necessary, which is the biggest bottleneck right now.