Final answer:
The SOHO router feature that simplifies IP address configuration for clients is the DHCP server, which automatically assigns IP addresses to devices.
Step-by-step explanation:
The feature of a SOHO router that simplifies IP address configuration on the private network for both wired and wireless clients is a DHCP server. DHCP, which stands for Dynamic Host Configuration Protocol, automatically assigns IP addresses to devices on the network. This simplifies the network setup process because the user does not have to manually assign IP addresses to each device. This feature is essential in ensuring that devices can communicate with each other and access the Internet without IP conflicts.