For OSPF adjacency to form, the authentication type and key must match on both routers for interfaces connecting to each other. In the NY configuration, the router is using MD5 authentication with a message digest key. Therefore, to make the LA router's configuration compatible, you need to configure interface E 0/0 on the LA router with 'ip ospf message-digest-key 1 md5 Cisco123' (option C) to match the MD5 key and authentication type. Additionally, enabling message-digest authentication under the OSPF routing process in LA (option D) ensures that the same authentication type is configured at the router level for the area. Together, these changes bring up the OSPF adjacency.