This shows that the server is running a newer, stricter version of SSHd that fails when our client tries a less-secure key exchange – the generic ‘Diffie-Hellman group exchange’. Not to worry, we just tell putty to propose a stricter key exchange with the server, namely the ‘Diffie-Hellman group 14’ algorithm.
Select it, click the [Up] button to move it to the top of the list. Done. Retry your connection.
This shows the corrected settings (after moving group 14 to the top).