The typical MySQL installation allows the database and the schema to be reachable only from localhost.
To verify if a database server is reachable from an outside host try this command on an external host:
telnet <database_server_hostname_or_IP> 3306
In case of a reachable problem, read below (Resolution for localhost only reachable problem).
Another possible problem is the firewall on the database server host. In this case, configure it to open the port 3306.
Launch MySQL Administrator GUI and insert access credentials (typically "root" and the corresponding password).
On left panel select "Startup Parameters" (if requested select "mysqld" and not "mysqld_safe"). On the right panel select "Advanced", scroll the window down and enable (if it's not) "bind to IP" parameter inserting "0.0.0.0" value (the database server is now open to any host, though you can limit it to a single IP). Save changes clicking on "Save Changes".
Restart MySQL Server. Refer to you DB Administrator about the correct procedure for instance shutdown and restart.
The MySQL configuration file must be edited (see How to Locate MySQL Configuration File).
Search inside the file for "bind-address" parameter (typically value is "127.0.0.1") and modify it to:
bind-address = 0.0.0.0
Save the file and restart MySQL Server. Refer to you DB Administrator about the correct procedure for instance shutdown and restart.