Thank you for the help. Should have checked here before calling Apple Support. Your fix worked just fine. I am using High Sierra OS.
Spent hours with Apple support on phone. Suggestion was to take the phone to an Apple Store and see if it worked on their computer. I told the support person that it was strange that two phones and two computers had the same problem. Phones connected to the USB port. This was confirmed in "system report".
After hanging up I tired hooking up my ipad which was not updated to IOS 12.0, and it connected. Also connected an iPod and old iphone 4 I use for storing and playing music. This confirmed to me that it was a compatibility problem with itunes and OS 12.0 software. I googled the problem and found your post.
This is the first time some one at Apple support did not have a clue about this software problem and did not know how to fix it. I only found out about this because I wanted to back up my iphone to my Macbook before trading it in for a new XS model. Not so sure I want to rush out and spend $1,000 after this experience.