It's possible to force the user to supply a password to encrypt RAR archives so a file can be extracted. If you have an encrypted archive for which you don't know the password, or if you've simply forgotten a password you assigned yourself, there are a handful of tricks you can attempt.
Check the source of the archive. If you downloaded it from a website, look around the site for a mention of the password (after all, it's unlikely someone offered an unopenable archive for download.) If the person you downloaded it from can be contacted, send them an email asking for the password.
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Try a few likely-seeming passwords. The name of the source website may work, as may the name or Internet handle of the archive creator.
Try a brute-force approach. This involves simply cycling through every possibility, one by one, until something works. You can technically do this yourself, but it would take forever and be extremely tedious. Fortunately there's a program that'll automate the process. The next few steps describe how to use RAR Password Cracker.
Download RAR Password Cracker from the link in "Resources" and double click the downloaded EXE to install it.
Run RAR Password Cracker and click "Load RAR Archive", then browse to and select the encrypted archive. Select a file from the archive and click "Add to Project", then click "Next".
Select "Brute Force Attack" and click "Next". Set a "Maximal length", the maximum number of characters you think are in the password, and a charset, which is the characters the password is likely to use.
Click "Next", then "Finish", The process will probably take a while.