how do i recover lost admin password

There are multiple ways to reset lost admin password and it varies in different situation. If you did not set any Firmware password and the FileVault was not turned on you can follow one of the steps mentioned below to reset Mac admin password.

1. Using Recovery Mode

Restart your Mac while holding the Command+R keys at the startup. Select English as your main language.

2. Go to Utilities Menu at the top and select Terminal.

3. Type "resetpassword" > Select hard drive partition containing the user account.

4. Select the username and click next > type a new password and confirm it

5. If you are running OS X 10.11 and above you may need to verify with your Apple ID password while resetting the password.

Using Single User Mode:

1. restart your Mac while holding the Command+S keys together and wait until the white text stop scrolling across the black screen.

2. Type command "fsck -fy" to check the hard drive for errors.

3. Type the following command

mount -uw /

4. Type command "ls /Users" and note down the short username you want to change the password for.

5. Type the following command replacing the shortusername with the actual username on your Mac account.

passwd shortusername

You can refer to the article Reset Mac Admin Password | Different method to reset Mac password for more detailed information as they have put all the possible method to reset mac admin password together nicely. There could be different methods to reset password in case the Filevault is on and a different metod to reset password in OS X 10.5, 10.6 and 10.9.