It sounds like something specific to RedHat 6. Perhaps the mysql config file is different than in CentOS. The error is basically saying it can't connect to MySQL to load the default database. It could be any number of reasons why it can't connect. Check a few things first:
Type (as root)
And see if the database actually starts. If it doesn't start, we'll need to find out why. If it does start, try to login using
What happens when you try those things?