Transit in Beijing. Terminal 2 and 3

No, you don't. You will be definitely eligible for 24 hour visa free transit (this is not a visa), so you don't need any kind of visa at all.

You will print out your flight tickets and have those printouts with you. Also, you will declare at check-in in your origin country that you will travel to X country via Beijing using 24 hours visa free transit.

Upon arrival in Beijing, you will approach 24 hour visa free transit counter and apply for a temporary entry permit that will allow you to transfer between the terminals.

That's it.

Thanks. So after arriving to Beijing I need to go firstly to 24 hours visa free counter and after that to immigration?

Exactly.