ORA-00905: missing keyword when trying to create a synonym
As the documentation says implicitly, you can create synonyms in the current DB only. So the first @PACOMNET in the synonym name is unnecessary (and causing the error). You should instead connect to the PACOMNET database and run

CREATE SYNONYM B2H.BILLING_USER_ACTIVITY
FOR B2H.BILLING_USER_ACTIVITY@PACOMNET.US.ORACLE.COM;