Mobile: Moto X2nd Generation OS: Android 6
My phones display not working, I am able to unlock it and touch is working.
Is there any application by which I can cast my phones display on my computer?
Vysor could solve your problem, it's available as a browser extension for Chrome or a standalone application for the three different operating systems: Windows, Mac and Linux.
Note: USB Debugging should be enabled. If your USB debugging is not enabled, I suggest to look for another similar phone to simulate touches in order to activate USB Debugging.