Why is my iPhone 6s shutting off during update? How do I solve this?

Update your device using iTunes

If you can’t update wirelessly on your iOS device, you can update manually using iTunes on a computer that you trust. If your computer is using Personal Hotspot on the iOS device that you’re updating, connect your computer to a different Wi-Fi or Ethernet network before you update.

1. Install the latest version of iTunes on your computer.
2. Connect your device to your computer.
3. Open iTunes and select your device.
4. Click Summary, then click Check for Update.
   
5. Click Download and Update.
6. If asked, enter your passcode. If you don't know your passcode, learn what to do.

If you receive any alerts or error messages, the article above links to this second help article stating:

If you see error messages in iTunes or need more space to update

Get help if you see error messages while updating your device with iTunes. Or if you need more space for an update, you can delete content from your device manually.

If you still have issues or are still unable to update your iPhone, please try the troubleshooting in this help article: If you can't update or restore your iPhone, iPad, or iPod touch
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