To root your phone manually, you need to turn on USB Debugging.
- Go to Setting, Find kernel version in About.
- Tap it seven times, at which point you should see the message, "You are now a developer!" With that done, tap Settings, About Phone, Developer Options, and then tick USB debugging." Then tap OK to approve the setting change.
- Now turn it ON in fastboot mode and unlock the bootloader.
- Install a recovery to help you with flashing.
- Flash a supporting custom ROM and gapps.
XDA Developers is a great site to help you with the process, support and Custom ROMs.
Check the below video for One click root method that works on many latest devices:
You can find all the specs here: Asus Zenfone Max Shot