How do I resolve this issue?
The user "root" doesn't have permission to access your database from that IP. I recommend creating a user specifically for Magento.
Login to your mysql account or ask Linode support to reset your mysql root password to something you can access.
$ mysql -u root -h 188.8.131.52 -p
Enter the password for your root user provided by Linode. Once logged in you'll see the mysql> prompt.
mysql> create database magento;
mysql> create user magento;
Based on your screen cap, I'd set your magento user up this way:
mysql> grant all on magento.* to 'magento'@'li1525-116.members.linode.com' identified by 'YOUR_PASSWORD_HERE';
(replace YOUR_PASSWORD_HERE with a more complex password.)
mysql> flush privileges;
You should now be able to use the following credentials when setting up Magento:
Database Server Host: 184.108.40.206 Database Server Username: magento Database Server Password: YOUR_PASSWORD_HERE (whatever you set this to) Database Name: magento