can I delete an Admin user?

I'm finally letting go of my A1278 model and that is the reason why I want to delete the Admin user. I want the other guy to create his own admin user and I have searched on how to delete it but nothing has worked. For now, I will give him my username and password.

This is what is recommended before giving away/selling a Mac.

Selling old Mac (4) Apple support

You can delete an Admin user or any user, but this requires at least one other account from which to do this.

So log out and into that other account that must have Admin privileges to allow the deletion and you can delete the other user account from within Sys Prefs > Accounts panel by selecting the user and clicking the minus sign underneath.

If you manage to delete your Admin account you will have a system that can no longer be upgraded, and you may even find you cannot install new software.

And of course you will always have the 'root' account that it totally unrestricted. By default it does not have a valid password, so you cannot login to the root account, but it MUST exist or you will not be able to boot the system.

If you manage to delete the Admin account (without having another Admin account), then you will need to figure out how to give the root account a valid password anytime you want to perform an upgrade, or install software that needs to be stored in privileged Folders. And then login as root. And if you want to keep others from using root when you are finished, you will then have to figure out how to take away root login access again.

All in all, it might be better if you tell us why you want to get rid of the Admin account, and perhaps someone can suggest alternative ways to achieve your goals without deleting the Admin account.