To install a custom rom you must have unlocked your bootloader. However for Sony phones, the process is a little more work. Sony has a website that provides IMEI code that you can use to unlock.
This is how you unlock the bootloader:
Simply go to the stock Sony dialer and type ##7378423## to access the service menu.
Tap Service info > Configuration > Rooting Status. If Bootloader unlock allowed says Yes, then you can continue with the next step. If it says No, or if the status is missing, your device cannot be unlocked.
This link will provide further instructions to get the IMEI number:
I see that you already have downloaded the custom rom into the phone. Although when unlocking bootloader, the device storage will be wiped and factory reset. Make sure to do a backup of important files. (SD card remains untouched)
Have the custom rom on the computer for later transfer.
To install the custom rom, you must have a custom recovery; TWRP for instance.
After this process, you will be able to flash any custom rom of your choice.
Simply follow this tutorial to manually flash the TWRP recovery:
After this part, the only thing remaining is to flash the custom rom. In TWRP, choose flash from storage and navigate to the rom file. Remember to wipe dalvik cache after flashing to get a stable boot. Note that first boot may take a while longer, so there is no need to worry.