Macbook air password reset problem

If you don't have your recovery key it can be a hassle to reset the password but lets give it a try

Try to reset your password using your Apple ID

Option 2: reset using your Apple ID

1. If you see the option to reset using your Apple ID, click it.

• • If your Mac restarts, follow the steps for Option 1, above.
  • If your Mac doesn't restart but immediately asks for your Apple ID, enter that information and click Reset Password.

1. If you're asked to create a new keychain to store the user's passwords, click OK to restart your Mac.
2. If you're asked to select an admin user you know the password for, click “Forgotten all passwords?”.
3. If you see a Reset Password window with the option to Deactivate Mac, click Deactivate Mac, then click Deactivate to confirm. This is temporary.
4. Enter your new password information, then click Next.
5. If this window lists multiple user accounts, click the Set Password button next to each account name, then enter the new password information for each account.
6. When the password reset process has been completed, click Restart.

If this is not working, please try this

Determine whether you're using a Mac with Apple silicon, then follow the appropriate steps to start up from macOS Recovery:

• Apple silicon: turn on your Mac and continue to press and hold the power button until you see the startup options window. Select the gear icon labelled Options, then click Continue.
• Intel processor: turn on your Mac and immediately press and hold Command (⌘)-R until you see an Apple logo or other image.

If you're asked to select an admin user

If you're asked to select an admin user you know the password for, click “Forgotten all passwords?” and proceed as described below.

If you're asked for your Apple ID information

Enter your Apple ID information. You may also be asked to enter the verification code sent to your other devices.

If you see an Activation Lock window, click Exit to Recovery Utilities. Then continue as described in the next section, “Use the Reset Password assistant”.

If you're asked to select a user that you want to reset the password for:

1. Select the user, then enter your new password information and click Next. 
2. After authentication has been successful, click Exit. 
3. Choose Apple menu  > Restart. The password reset process has been completed, so you don't need to take additional steps.

You should now see the utilities window, which shows options such as restoring from Time Machine, reinstalling macOS and using Disk Utility.

1. From the Utilities menu in the menu bar, choose Terminal.
2. In the Terminal window, type resetpassword, then press Return to open the Reset Password assistant.
3. If you're asked to select an admin user you know the password for, click “Forgotten all passwords?”.
4. At the Reset Password window, click Deactivate Mac, then click Deactivate to confirm.
5. If you see an Activation Lock window, enter your Apple ID email and password, then click Next.
6. At the Reset Password window, enter your new password information, then click Next.
7. If this window shows multiple user accounts, click the Set Password button next to each account name, then enter the new password information for each account.
8. When the password reset process has been completed, click Exit.
9. Choose Apple menu  > Restart, then log in with your new password.

If you still cannot reset your password, the only way is, unfortunately, to erase your mac

If you still can't reset your password, erase your Mac

If no other solution is successful, you have the option to reset your password by erasing your Mac.

1. Shut down your Mac, then start up from macOS recovery as described previously.
2. When you're asked to select an admin user you know the password for, choose Erase Mac from the Recovery Assistant menu in the menu bar.
3. From the Erase Mac window, click Erase Mac, then click Erase Mac to confirm. 
4. If your Mac restarts to a flashing question mark, press and hold the power button for a few seconds until your Mac turns off.
5. Start up from macOS Recovery again, then reinstall macOS. For details, see How to reinstall macOS. 

If you can't reinstall macOS because the installer can't see a hard disk on which to install, you may need to change the format of the disk:

1. Press Command (⌘)-Q to quit the installer.
2. When you see the utilities window, select Disk Utility, then click Continue.
3. Select the first item listed in the sidebar of the Disk Utility window. This is your built-in hard disk.
4. Click the Erase button or tab on the right-hand side of the window, then enter these details:

• • Name: Macintosh HD
  • Format: Mac OS Extended (Journalled)
  • Scheme (if shown): GUID Partition Map

1. Click Erase, then click Erase to confirm.
2. When the erase process has been completed, press Command-Q to quit Disk Utility and return to the utilities window. You should now be able to reinstall macOS successfully.

If you still need help, please contact Apple Support.

See this link for further information

https://support.apple.com/en-gb/HT212190