Their server probably has a mod_security rule that's flagging something submitted in the parameters on that page, thus throwing the 406 error.
You can temporarily get around it by adding the following to the /admin/.htaccess file (create one if it doesn't already exist):
Code:
<IfModule mod_security.c>
# SecFilterEngine Off
SecFilterScanPOST Off
</IfModule>
If that doesn't make it work, try removing the #
If that doesn't work, you'll have to check the server's errorlogs for the specific reason for the 406, and then talk to the server administrator (hosting company) to fix it.