Oracle, how to manually re-instantiate a PL/SQL package

You should be able to backup an 11.2.0.2 database using RMAN with an RMAN repository that is set to 11.2.0.4. There seems to be some invalid objects in your RMAN repository schema. You may want to try compiling all of the invalid objects in your RMAN repository to see if they become valid. This probably has nothing to do with you backing up an 11.2.0.2 database with an 11.2.0.4 RMAN repository.

I am suspecting with the case sensitive name or special character(i.e. ' or white-space) included with the package name unknowingly while creating package. I tried to get object name from dictionary itself which ensures correct object name in your drop command in the following script, it can help in your context:

select 
'DROP PACKAGE ' || '"' || OBJECT_NAME || '";' as "Command" 
from 
USER_OBJECTS 
WHERE 
OBJECT_NAME LIKE '%POSTING_PROCS%'
AND OBJECT_TYPE='PACKAGE';

CAUTION - REMEMBER THAT ABOVE SCRIPT GENERATES DROP COMMANDS WHICH CAN CONTAINS POSTING_PROCS AS THE PART OF OTHER PACKAGE NAME, PLEASE CHECK EACH DROP STATEMENTS BEFORE EXECUTING THEM IN YOUR SERVER.

Alternatively - You might be using client tool like TOAD, SQL Tool, SQL Developer which display your invalid object name in a GUI format. You can try to delete your object by right click on the object and follow with the drop option.