This article explains how to permanently deactivate an account on Reddit.
Steps
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Step 1. Open
You can access the site using any browser you wish.
If you are not logged in to the account you want to delete, enter your username and password
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Step 2. Access your account settings by clicking on "Preferences"
It is located at the top right.
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Step 3. Click on the Call Disable tab
It is the last entry at the top of the screen.
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Step 4. Enter your details, ie username and password, in the appropriate fields
This will confirm that the account belongs to you and you have not simply opened the profile of a person who forgot to log out.
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Step 5. Check the confirmation box
It is next to "I understand that deactivated accounts cannot be recovered". This will confirm that you actually want to delete the account.
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Step 6. Click Deactivate Account
At this point it will have been deleted from Reddit.