No option for two factor authentication

Check the availability of two-factor authentication for your device and on how to set it up Two-factor authentication for Apple ID https://support.apple.com/en-us/HT204915  See this section especially 

Set up two-factor authentication for your Apple ID. From this section, "Two-factor authentication is available for Apple ID accounts with at least one device that's using the latest iOS, iPadOS, or macOS. Learn more. You can follow these steps on your iPhone, iPad, or iPod touch to turn on two-factor authentication."

Not all Apple ID accounts can use 2 Factor Authentication. If the posts above do not explain why you can't enable 2 Factor Authentication, contact Apple ID Support. 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. 

Apple Support schedule phone call

https://twitter.com/AppleSupport

See the article https://support.apple.com/en-in/HT205075