When I try to enter a user password to delete an account, it doesn't work. and I know the password I'm using is correct
If you can't delete the user for some reason, you can remove it at the command line.

Launch "Terminal" (from /Applications/Utilities/Terminal.app, or search via Spotlight) and type:

sudo dscl . list /Users


...followed by your administrator password.  Then hit enter

The output will show you the shortname of your local users (towards the bottom).
Here I called the user to be removed "testy" (I'm only showing the last few entries):

...
admin
daemon
Guest
nobody
root
testy


Now remove the user from your system and from System Preferences (exchanging the shortname "testy" with your own, found earlier):

sudo dscl . delete /Users/testy


Then hit enter.

The home folder of that user you can either keep, if there are important files, or delete it with...

sudo rm -r /Users/testy 


...and again hit enter.

PS. A speculative answer for the permissions error received and mentioned in the comments section can be found at StackExchange:
What causes eDSPermissionError when running dscl?