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Get a verification code and sign in with two-factor authentication - Apple Support

You need another trusted device or telephone number.

See Two-factor authentication for Apple ID - Apple Support:

A trusted device is an iPhone, iPad, or iPod touch with iOS 9 and later, or a Mac with OS X El Capitan and later that you've already signed in to using two-factor authentication.

If the steps in the first article Kappy posted don't help, see the account recovery section near the end of the article.

The Recovery Process is an automated process and length of time it takes can vary a lot. Apple ID Support can only answer your questions. They can't intervene in or speed up the process. The article below has some suggestions to shorten the the time the process takes.

Apple ID - Recover your Apple ID with two-factor authentication account recovery.