I do not have the phone number that is used for two-step verification of Apple ID. How do I log in?

OK: you kept saying it was two-step verification but now the image you've just posted says it's two-factor authentication. If you give me wrong information it's inevitable that I give you the wrong answer.

Apple's page at https://support.apple.com/HT204915 says:

If you can’t sign in, access a trusted device, reset your password or receive verification codes, you can request an account recovery to regain access to your account. Account recovery is an automatic process designed to get you back in to your account as quickly as possible, while also denying access to anyone who may be pretending to be you. It may take a few days – or longer – depending on what specific account information you can provide to verify your identity.

If you've generated a recovery key, you can use your recovery key to regain access to your account instead. Find out more about using a recovery key. 

So assuming you don't have a recovery key, follow the first link in that information.

Additionally, Apple say 'Find My iPhone notifications can be used to receive verification codes on any iOS device with Find My iPhone turned on. Learn how to set up Find My iPhone.' If you haven't already set this up it may or may not be possible in the current situation.

As I already said, you use the password and the Recovery Key you were given when you set it up (and told to keep in a safe place).

Assuming this is indeed two-step verification and not two-factor authentication, if you don't have the registered phone you should use the Recovery Key you were given when you set 2SV up.

Two-step verification for Apple ID - Apple Support

Are you sure it's this process? If it's two-factor authentication (which is now the recommended method) you should get codes sent to all trusted devices, or you can request an account recovery to regain access to your account.