can you restore a new iphone 6 with a backup from and iphone 5c on itunes at an apple store?

If you bring your computer with you, yes.

their itunes does not have credentials to show your iphone as the home computer do. so i suggest you to have an icloud back up so you can back up online

pieohpie wrote:

can you restore a new iphone 6 with a backup from and iphone 5c on itunes at an apple store?

What you're trying to do is completely impractical and unnecessary.

pieohpie, you should backup your iphone 5c with itunes firstly, and then you can connect your new iphone 6 to the same computer and restore the backup to your new iphone 6 with itunes.

See: iPhone: Transferring information from your current iPhone to a new iPhone

You cannot use an Apple Store computer to back up your data. It is your responsibility to back up YOUR data before going to an Apple Store. This is to protect your private data.