How to downgrade from ios 7 to ios 6.1.3 on iphone 4?

I have tried restoring my iphone 4 many times and I have also got the latest version of iTunes but whenever I try to restore the iphone, my computer says that there was an error in restoring the iphone. Can someone help me on how to restore my iphone because I have watched all the videos on youtube and the only thing that happenes is that there's always an error that occurs in the middle of the procedure. Can someone please tell me how to stop this error and properly restore my iphone 4.

Not possible anymore. You used to be able to backup your SHSH blobs with Cydia if you jailbroke but Apple verifies each software update. IOS 7 was designed with the newer models in mind, but they extended support to the iPhone 4, which was a bad idea. You may have to wait for a patch or something.

The last time I took the time to read the End User License Agreement for iOS &, it said that once this Upgrade is done, there's no way to roll back to an older version of iOS 6, or older.

But, it sounds like you are between a rock and a hard place.

Fortunately, you're iPhone 4 is still PORTABLE. So take it back to the store where you bought it, and they will re-install iOS 7 for you (and, likely NOT for free).