Hi swati54,
Your Mac is asking for a FileVault recovery key. This recovery key is specific to your Mac, and only your Mac can generate it (when you first set up FileVault).
FileVault protects the data on your Mac by encrypting (scrambling) it, so that your password or the recovery key are required in order to decrypt (unscramble) it. This prevents thieves from accessing your data, but it also makes it harder to reset your password.
FileVault is not enabled by default, but it can be enabled from two places:
- The Setup Assistant - if the option appears to enable FileVault and you choose to do so
- In System Preferences -> Security and Privacy -> FileVault.
Unfortunately, if you don't have your password or recovery key, and you chose not to store your recovery key in iCloud when you set up FileVault, the only remaining option is to erase your Mac and start over.
To erase your Mac and reinstall macOS:
- Start up from macOS Recovery.
- If you're prompted for an admin password or the recovery key, skip to step 5.
- The main utilities window should appear. At the top of the screen, select Utilities -> Terminal.
- Type this command and hit Enter (Return): resetpassword
- At the top of the screen, select Recovery Assistant -> Erase Mac.
- Follow the onscreen instructions to erase and reactivate your Mac.
- The main utilities window should appear again. Select Install macOS and follow the onscreen instructions. Depending on Internet speeds, this could take quite a while - your Mac will need to download 12 GB over the Internet.
If you made a Time Machine backup prior to this incident, you can restore from that backup after you erase and reinstall macOS.