When trying to install the Exchange 2010 on Windows Server 2012 there is a few more tweaks that need to be made in the registry before you will be able to complete the Mailbox Server Role!
Exchange 2010 SP1 & SP2 Mailbox Role failed on Windows Server 2012.
See the below error.
Error in Setup Logs.
To Fix this issue, Find the Reg Key mention in the setup logs(In Blue).
Located the below registry key as per the error
It will look like this.
Now Copy Microsoft-Windows-ApplicationResourceManagementSystem, and add the value it into the Default key of 0 & 1, see below
Once this is done run the Exchange 2010 setup again and it will complete fine.