Linked server to remote sql server failed
As I can see from the your error messages you are connecting to the server from different domain. So your cuurent windows credentials cannot be used as Be made using the login’s current security context implies.

Option Be made using this security context implies that during authentication SQl Server will use the credentials specified in the text boxes (SQL Server authentication).

So the answer is - you can use the method Be made using this security context with the credentials you specified, or, alternatively you can specify how every local user will authenticate on the remote server (specifying that no authentication is made for any login not in the list above):