My Mac min 2014 shuts down half way through start up. I think I want to re install os 10.12.6
Did you try to use Recovery Mode to do that, as explained in this article?
About macOS Recovery on Intel-based Mac computers - Apple Support
Did you try to use Recovery Mode to do that, as explained in this article?
About macOS Recovery on Intel-based Mac computers - Apple Support
Try booting into Safe Mode in case some third party software is causing a problem.
Try running the Apple Diagnostics to see if any hardware issues are detected. If your Mini is using a hard drive, then there is a good chance the drive is failing. Unfortunately the diagnostics don't detect most drive failures. Let me know if you would like instructions for creating & using a bootable Linux USB stick to check the health of the drive if none of the other suggestions help.
Mac min 2014 won't start up
