With those errors, you normally only need to carefully read line 1.
include(Meanbee/Royalmail/Model/Shipping/Carrier/Royalmail/.php) [function.include]: failed to open stream: No such file or directory
So what is it saying? It’s trying to open a file but can’t find it.
So which file is it looking for? “Meanbee/Royalmail/Model/Shipping/Carrier/Royalmail/.php”
Does anything seem out of the ordinary? Can you see this file over FTP / on the command line?
I bet you you can’t, I highly doubt there’s a file just called “.php” in the RoyalMail folder.
So it seems somewhere in the code, they’ve misstyped the file name. It should either be Royalmail.php or Royalmail/something.php
The answer will be whatever the coder of this module says it is, so ask Meanbee I’d say. Or check a previous version of that Module and compare the files with Beyond Compare. Or go through the installation manual again to see if maybe you yourself mistyped something.
But whatever the solution, the problem report says exactly and clearly what’s wrong.