My i phon 12 pro was updated but when i want to install an application(google search) written need to up date 15/0 o later for what??

The current version for the iPhone 12 Pro is 17.2. If you go to Settings/General/Software Update it should be offered to you. To update over the air from the phone all of these requirements must be met:

• You need at least 10 GB of free storage for iOS 16 and later or 6 GB for iOS 15 or lower; more is better
• You must be connected to a Wi-Fi network (and not a personal hotspot) unless it is an iPhone that supports cellular 5G (12, 13, 14, 15 or SE 3rd edition) and has a 5G network connection
• The phone must be charged to at least 50%, and preferably plugged in so it stays above 50% during the update
• The phone must not be in Low Power Mode
• The phone must not be connected through VPN, and it may be necessary to delete any VPN apps and VPN profiles
• The phone cannot be in Airplane mode and must have a cellular data connection
• You cannot still have a beta of a previous version installed on the phone
• You cannot have a previous version that was downloaded, but not installed - go to Settings/General/iPhone Storage to look; if you find an iOS installer, delete it

If you can't meet all of them you can still update using your computer.