So if your using Moto g 2015 XT1069 [Titan] on android lollipop 5.1.1 then you can update your device to android marshmallow 6.0 officially by downloading the ota update of moto g 2nd gen XT1069 and install it in your device.
Note that this ota update will only work for XT1069.
#How to Install the official Marshmallow 6.0 in Moto g 2nd gen 2014
2.Put the zip file in internal memory then reboot your device.
3.Navigate to settings -> about->Check for Update
4.You will see a notification showing a new System software update system version 22.56.3 is available like below image.
5.Then tap on Yes,I’M IN and select Wi-fi or Mobile Network and tap on DONE ! Your Update will start downloading.
6.After downloading the update it will automatically reboot your device and install the system update.
7.It will take at least 15 min to update your device or more.After installing the update your device is ready to Use.