Which configuration enables Telnet access to RouterX using the router username/password database for authentication?

The correct configuration is line vty 0 4 followed by login local. The line vty 0 4 command accesses the Virtual Terminal lines, which are used for Telnet and SSH access. The login local command instructs the router to authenticate users attempting to connect via these VTY lines against the local username and password database configured on the router. The incorrect options are: line aux 0 configures the auxiliary port, not for remote Telnet access. aaa new-model and aaa authentication login auth-list local configure AAA (Authentication, Authorization, and Accounting), which is a more advanced authentication method. While valid for authentication, it's not the most direct answer for using the router's local database for Telnet when login local is available and simpler. login without local would prompt for a password but wouldn't explicitly use the local database unless a global login authentication default or similar AAA configuration was present. login local specifically directs it to the local user database.