You want to enable archiving on your database. Presently, the database is running in NOARCHIVELOG mode. Given below are the steps to accomplish the task in random order: 1. Shut down the instance…

This sequence treats step 4 (DB_RECOVERY_FILE_DEST) as required, but it is not mandatory for enabling archiving since LOG_ARCHIVE_DEST_n parameters are a valid alternative archive destination.

This sequence includes step 4 as required and places it after mounting, but DB_RECOVERY_FILE_DEST is optional and omitting it does not prevent ARCHIVELOG mode from being enabled.

The correct order is shut down (1), start up and mount (3), execute ALTER DATABASE ARCHIVELOG (2), then open (5). The database must be in MOUNT state for ALTER DATABASE ARCHIVELOG to succeed. Step 4 (DB_RECOVERY_FILE_DEST) is not required because LOG_ARCHIVE_DEST_n parameters can designate the archive destination instead.

This sequence omits step 3 (mounting), but ALTER DATABASE ARCHIVELOG cannot be executed unless the database is in MOUNT state - running it on an open database will fail.

This sequence omits step 2 (ALTER DATABASE ARCHIVELOG), which is the mandatory command that actually switches the database from NOARCHIVELOG to ARCHIVELOG mode.