How to "safely" root a Motorola XT320 (running Android 2.3.6 / Gingerbread) without loosing data?
There are a few options. But you need to be cautious and do a little bit research before choosing one.

Step 1. Back up all your data to pc or sd card (if sd card then better remove it after backup is complete). For pc you can use tools like moboginey pc suit.

Next you can use one click root functionality of mobogine. Or try following guidelines here - https://www.oneclickroot.com/root/motorola-xt320-tnbst_4_07-23-15rps-2-3-6/