Desk jet 4200 e not displaying on my iPhone when it’s printing

Just to be sure you didn't miss anything when setting up your HP printer for AirPrint, please take a look at the following HP support article/YouTube video. Although the first link is specific to setting up the printer for a Mac, it still show how to properly set it up for a wireless network ... which is required for both it and your iPhone to work with. The second link is specific to iPhones & iPads.

• https://support.hp.com/in-en/contact/solution/printer/airprint
• https://support.hp.com/hk-en/document/ish_1946968-1947068-16