If you have a valid recovery code, you should be able to access your account without issue.

1. Go to https://accounts.firefox.com and login.
2. If you are prompted for a two-step authentication code, click Use recovery code and enter one of your saved recovery codes.
3. Expand the Two-step authentication section by clicking {button Change}.
4. Click Disable.

For more information, see What if I'm locked out of Two-Step Authentication?

Hope this helps.

Note that the user wrote in the title: How to Recover Sync account without 6 and 10 digits code?

I don't think that without recovery it won't be possible to access the account and you may have to setup a new account using a different email address.

No, I can´t because I have a "Recovery Key" (32 digits) and not a "Recovery Code" (10 digits)

I think that the 32-digit recovery key only allows to bypass a lost/forgotten password (password reset) and that you would still get the 2FA prompt to be able to continue. I haven't tested or experimented with this because of the possibility to lose access to the account.

I thought that the 32-digit recovery key was the only thing needed, and indeed was the only key that I wrote as a "backup". I didn't think that Firefox and Sync changed a lot since 2015 (today I installed a clean version of Windows), that's why I can't login again, and I don't have another device signed in.

2FA adds an extra security layer in addition to the name and password. It is not possible to circumvent this without recovery codes once 2FA is enabled. You can consider to backup the TOTP QR code (otpauth://) to be able to reinstall the authenticator.

cor-el said

You can consider to backup the TOTP QR code (otpauth://) to be able to reinstall the authenticator.

And this is how? The TOTP QR code is from the previous Windows installation? (that I don't have) or is generated from a third party app? https://stefansundin.github.io/2fa-qr/

Why do I have to use a different email address? Why can't the firefox person who created all this technology delete my account and release my email address?

How can I contact an actual support person from firefox accounts?

Pratyush Tewari said

Why do I have to use a different email address? Why can't the firefox person who created all this technology delete my account and release my email address?

Because without access to your account there is no way to verify that you are the legitimate owner of that Firefox Account. Simply proving you have access to the email address is not sufficient.

This is to protect against a number of situations. What if someone hacks your email and wants to get access to your Firefox Account? What if you simply deleted your email address and it was recycled and claimed by someone else.

The points of the recovery code is to get past situations like this, which is why it's very important to keep it.

At the present time, there is no one you can contact that can manually delete Firefox Accounts.

I understand the security aspects. But you think it is wise to keep creating multiple email addresses just to have a firefox account?

I am sure when you get into this situation then you'll realize that this is a horrible approach to handling security. Just lock everything and make it unusable. You'll be as frustrated like me as well in that case. My hard drive crashed where I stashed the recovery code and now I have to create a new email address and remember those credentials and burden myself even more than I already am?

These software engineers do not understand how humans work! In order to make a better design, you should look into all the edge cases and not just make a horrible decision that is simple for them to code.