To install the php-mbstring on Red Hat Enterprise Linux 6 you have to add a new software channel to the system through the Red Hat Customer portal.
1. Log into RHN via rhn.redhat.com
2. Navigate to Subscription->RHN Classic->Registered Systems
3. Select the desired system from your list
4. Navigate to Software->Software Channels
5. Check the box next to RHEL Server Optional
6. Click on Change Subscriptions Button
7. Now, log into your systems cli and perform the following steps.
8. Synchronize the system’s profile
sudo rhn-profile-sync
9. Perform an update to yum
sudo yum update
10. Now install the php-mbstring package
sudo yum install php-mbstring
11. Restart apache
sudo service httpd restart
All Done!
Source: http://www.sysarchitects.com/php_mbstring_on_rhel6