Have you got 32 bit or 64 bit?
What versions of sofware?

#uname -a
#rpm -qa | grep php
#rpm -qa | grep mysql

I created the database and user in mysql, still having issue.
Can you please post your steps on resolving this.

localhost did the trick.

I was failing to connect because of the wrong password. I had run as suggested this command from mysqladmin:

grant all privileges on freepbx.* to 'freepbx'@'localhost' identified by 'YOURPASSWORD';

However when run the install wizard it kept using a Password of 'freepbx'. I saw no place in the install wizard to change what password it used to access the database. Therefore I went to the file database.php, which in my case was located at /var/www/html/freepbx/freepbx/config/database.php, and edited the password there. If you look at this file it has

$config['default'] = array
(
'benchmark' => TRUE,
'persistent' => FALSE,
'connection' => array
(
'type' => 'mysql',
'user' => 'freepbx',
'pass' => 'YOURPASSWORD',
'host' => '127.0.0.1',
'port' => FALSE,
'socket' => FALSE,
'database' => 'freepbx'
),
'character_set' => 'utf8',
'table_prefix' => '',
'object' => TRUE,
'cache' => FALSE,
'escape' => TRUE
);

I just changed the line for password in here to match the password I set for the database and it worked no problem. I am not sure if I missed the spot to enter the password through the GUI or this feature has not been implemented yet.