Answer:
The method that allows connecting a private network to the internet without obtaining registered addresses for every host is Network Address Translation (NAT). NAT is used to map the private IP addresses on a local area network (LAN) to one or more public IP addresses that are routable on the internet. This way, multiple hosts on the LAN can share a single public IP address, reducing the need for registered addresses for each host. NAT operates by modifying the IP headers of packets that pass through a network gateway, translating the private IP addresses to the public IP address for internet communication.