Private IP means the router WAN IP is in the private IP range. This is because the ISP ran out of IPv4 addresses and therefore made several customers share the same public IP. Basically it's like a double NAT connection. You can't host anything with this type of connection because there is no public IP that can directly route to your router.

Public IP:
Internet----- (public IP) home router (private IP) ------ internal home network

Private IP:
Internet-------- (public IP) ISP router/NAT-------- (private IP) home router (private IP) ---------- internal home network

You are the only one that made sense in this thread with readers to your explanations.

Meanwhile, if one opts for IPv6.....better pray all devices have proper IPv6 firewall in place. All direct point-to-point connectivity with IPv6.
Last time, NAT 'accidentally' act as filter/firewall for IPv4, with IPv6....hmmm.....unless one can configure NAT-ed IPv6.......   but it is pointless in first place.