The installation of the RD Connection Broker Role Service can fail with the following error on Windows Server 2012:
RD Connection Broker Role Service: Failed
Unable To Install RD Connection Broker Role Service On <<Server>>
This issue came up in response to a question from Ridhuan Amri who was trying to install RD Connection Broker on a VMware VM. It seems that you are unable to install the RD Connection Broker on a server that has any Active Directory Domain Services installed.
To fix the issue, uninstall AD Domain Services from the server (or probably stand up a new server!) and try to install Remote Desktop Services again. Alternatively, I believe there may be a Windows Update available to fix this, so try patching your server before installing RD Connection Broker.