To permanently delete images from Lightroom and from your computer, highlight the image(s) that you want deleted and press the delete key. Choose the option to delete from disk. If you don't want them deleted from the disk and only from Lightroom, then choose the button to remove them.
To get rid of the catalogs that you are no longer using just go to the folder that contains the catalogs using Windows Explorer or Finder. Highlight the catalogs you are no longer using and delete them. This will delete the catalogs, but will have no effect on any of your images.
Thank you for your response and you assistance. I apologize for taking so long to get back with you but, I have been overwhelmed and my box flooded with all of the questions by other members of the various communities on here, thus it has taken me awhile to find my original question to you. I do not suppose you know if there is any way on my profile to delete the enormous amount of emails received from so many people, do you. I looked and looked but saw no where that offered a delete option for the emails in my box here. I did delete them on my Apple mailbox, but they still showed up here none the less. Any how, again, thank you for being so kind as to take the time to answer my questions.