Unable to install OS X El Capitan on my iMac with an unexpected error

Please read Writing an effective Apple Support Communities Question! Your post has no useful information, iMacs have been in production over 25 years as has Mac OS in hundreds of configurations. We have ZERO idea what you own, what version of Mac OS was installed or why would you do what you did. After reading the information in the link then please re-write your question and include useful information so we can get an idea of possibly how to help you out.

Any tom, dick or harry can write a tutorial so when writing things like "I watched a tutorial..." be specific!!!!!!!!!!!!!!!!!!!!!!!!!!

FYI:

Mac startup key combinations - Apple Support

How to reinstall macOS - Apple Support

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On an Intel-based Mac:

• If you used Command-R to start up from the local Recovery system, you get the current version of the most recently installed macOS.
• If you used Option-Command-R to start up from Internet Recovery, you might get the latest macOS that is compatible with your Mac. 
• If you used Shift-Option-Command-R to start up from Internet Recovery, you might get the macOS that came with your Mac, or the closest version still available.

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These days, I would not suggest relying solely on Internet Recovery for any really old Mac – say, one that shipped with anything before Catalina.

If you get this Mac running again, please consider putting a bootable copy of macOS onto an external HDD or SSD, so that in the event that something happens again, you have a working system to start up from while you try to fix things. That could be a bootable backup (Carbon Copy Cloner, SuperDuper!), or a clean install.

If you are trying to download macOS by any means than Internet Recovery, you generally need to have a Mac with a working copy of macOS to download and run the installer – or to follow a more involved process to make a bootable USB flash drive. (Reference: How to download and install macOS - Apple Support)

Too bad that this "tutorial" didn't mention that little detail before leading you down the "erase your Mac" path.

Here's a more readable version of the relevant part of your photo. Looks like the installer asked you to sign in with your Apple ID, and gave the "403 Forbidden" error while it was trying to validate the login.

"403 Forbidden" is a HTTP response status code indicating that "the server understood the request but refused to process it." (Although you were not running a Web browser, the Mac might have been using Web protocols behind the scenes.). I think this may mean that there is something more serious going on than simply entering an incorrect Apple ID password – although you could try doing an installation again, if you think that you might have entered the wrong password. Something on the server side that you can't fix.

The rest of the screen doesn't tell us anything about which Mac you have, or what versions of the Macintosh OS it can run. It does tell us that your main drive appears to be have a capacity of 128 GB. If this is a factory drive, that would possibly match an 21.5" Early 2013 iMac (the only one I see in MacTracker, with a "brushed aluminum" front, for which 128 GB (of flash storage) was an option).

But you really should tell us which iMac you have instead of keeping us guessing.

Try booting into Recovery Mode using Command + Option + R which should not require you to authenticate with the App Store to verify a previous "purchase" of macOS (at least according to a small not in Apple's older documentation).

Otherwise we definitely need to know the exact model of the Mac so we know which versions of macOS are compatible with it as it may allow you to create a bootable macOS USB installer if you have access to another compatible Mac, or to use an OS X 10.6 Snow Leopard DVD (there are several of them so we need to know the exact model here as well).

You can try getting the exact model my entering the system serial number on the Apple check coverage page here (please don't post the serial number on the forum as it is considered personal information):

Check Your Service and Support Coverage - Apple Support

Unfortunately the last older serial number I tried checking did not work on the Apple site, so you may need to use EveryMac.com to get the information (this tells you how little Apple values their older systems).