How to format my Mac?

The second technique is correct. Apple's Support document explains,

"Turn on your Mac, then immediately press and hold these two keys until you see an Apple logo or other image: Command (⌘) and R."

Use Disk Utility to erase an Intel-based Mac - Apple Support

I understand that is not working though. If you are using a desktop Mac that uses an external keyboard, try substituting another (preferably wired USB) keyboard. The same technique will work with any keyboard, wired or wireless, but it is possible that a wireless keyboard is not communicating properly while starting the Mac.

In any event you simply must find a way to start that Mac in Recovery mode before you can erase its startup disk.

Ok, I seem to recall reading (somewhere?) that if you are unable to get a Mac to boot Recovery, an SMC Reset is justified.

Try it: Reset the SMC of your Mac - Apple Support

Log in, then shut down your Mac in the usual manner, and then try Recovery again.

I'll keep thinking.

Do you want to erase it? Erase your Mac and reset it to factory settings - Apple Support describes how to do that.

Disk Utility (Levytyökalu) is one of the choices that appear upon booting your Mac in Recovery mode:

It seems that you are not even getting that far, so please back up a step and let us know which part of Use Disk Utility to erase an Intel-based Mac - Apple Support is not working for you.

Often, people don't hold the combination of keys in the correct manner or in the correct sequence, so all I can do is refer you to those Apple Support documents. I'm not at all implying you're doing anything wrong, but I'm at a loss to explain the reason it's not entering Recovery the way it should.

Yes, it is weird, but we simply must find a way to get that Mac into Recovery mode.

Please describe the specific step in the specific document that is not resulting in what you expect to see. Otherwise, continue to the end which states,

"If you need help, contact Apple Support."

This site is not Apple Support. To contact Apple Support, click that link.

Please read that entire document, all the way through and including its end. If you can't use Erase All Content and Settings includes the instructions you need to follow.