why do I not get verification code

See Get a verification code and sign in with two-factor authentication https://support.apple.com/en-us/HT204974  Below is an excerpt, but read the whole document. See the bold italics below.

Whenever you sign in with your Apple ID on a new device or browser, you'll confirm your identity with your password plus a six-digit verification code. There are a few ways you can get a verification code. You can use the code displayed on your trusted device, get a text or phone call, or generate a code from your trusted device [see the additional information in the article]. 

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 into using two-factor authentication.

If you can’t sign in, reset your password, or receive verification codes, you can request account recovery to regain access to your account. This link takes you to:

Recover your Apple ID when you can’t reset your password  https://support.apple.com/en-us/HT204921 which you may need to use.

“Account recovery might take a few days or longer, depending on the specific account information you can provide to verify your identity. After you request account  recovery, you'll get an email with a confirmation of your request and the date and time of when you can expect to regain access. … When the wait period is over, Apple sends you a text or automated phone call with instructions to regain access to your account.” Read the whole document carefully. 

Are you still using Mac OS X Yosemite see the article https://support.apple.com/en-in/HT204915

What are the system requirements for two-factor authentication?

• Mac with OS X El Capitan and iTunes 12.3 and later

You can generate a code from Mac itself .

Read https://support.apple.com/en-us/HT204974

contact Apple ID Support for assistance.  See the Apple Support articles below for contact information.  

Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.   (Link doesn’t always load)  

Get Support          Work through the screens to get a chat option. You may have to pick a slightly different problem.

Apple Support schedule phone call

https://twitter.com/AppleSupport.          People have posted it may take an hour or more to get a response.

In Mac OS catalina 10.15.6 when Apple ID and password is signed with www.icloud.com it prompts to enter admin password , don't enter it rather click on cancel .

Then enter Apple ID and password manually ( if iCloud Keychain is set up the credentials will fill up automatically ) .

Click on allow .

Slightly drag and drop the window of change password , click on don't change .

The verification window that was hidden will appear , a code will appear when the Mac is located through IP address , and location services / find my Mac is enabled .

Sometimes due to weak wifi signals , the code can be delayed then click on didn't get a verification , the code appears on Mac , use it and access the account also in this case devices are added in the Mac but not synced so the code will not appear in iPhone ( most important clue ) and Mac will act as device and create a code on desktop screen .

Regarding Mac OS Yosemite , the steps might differ as versions have been changed , the upcoming steps might have changed .

The step what I mentioned is when trusted numbers are added / and verified in the account , but they are not signed in with same Apple ID and password on the same network .

If Mac and trusted numbers are signed in with same Apple ID and password and are synced , the code can be generated from Mac or iPhone ( same method using maps , it will prompt to allow or don't allow ) .

If the question is for two factor authentication account , either the device iPhone is lost / damaged / turned off or the sim has been removed / not in service or broken and mobile number is not verified in the account .

It depends the account is set from iPhone or Mac .

I think you are using two step verification rather than two factor authentication account see this https://support.apple.com/en-us/HT204152