Does a "Hello" screen mean my iPhone was erased? I'm preparing to ship my old iPhone 6 to a new home. When I press and hold the lock button, a white screen saying "Hello" in various languages appears. Does that mean I erased all of my data? I haven't used the phone in months so I can't remember what I did to get the phone to that screen, but I want to be sure that my data is erased before getting rid of the device.

TL;DR Is it possible to get an iPhone to the white "Hello" set up screen without completely erasing the previous user's data?
The "Hello" screen does not necessarily mean you have erased the phone. It could just mean that iOS was updated. I would complete the setup steps (you can skip many of them) then go into Settings > General > Reset > Erase All Content and Settings to be sure. You will also need to remove the device from your iCloud account or it will be bricked to the new owner.