What do I do if the apple logo on my phone keeps popping up but my phone won’t do anything else?

Perform a Forced Restart on the phone. Follow the instructions very carefully, as this is a bit tricky. You may need to repeat this several times.

Force restart iPhone - Apple Support

There are only 2 possible results when you perform a Forced Restart:

1) The phone returns to normal operation.....or, if it doesn't.....

2) There is a hardware problem with the phone that will need attention at the Apple Store (make an appointment) or take the phone to an authorized Apple Service shop.

You can find a list of authorized service shops in your area using the link just below:

Find Locations

At this point, if major repairs are required.....as I suspect.....and since the iPhone 6 is really up there in years, the money might be better spent on a new phone.