If you check the screenshot you have sent us. On the left hand side you have the source from where you actually importing the Images and on the right hand side is the destination which you need to select that it should copy your images to that location (Which should be your Macintosh Drive or any external hard drive)
You can also try run the Disk Utility to repair the permissions. Refer: Repair disk permissions by running Disk Utility | Mac OS X
To the left my source is my Nikon and to the right I am trying to send them to Mac HD. Each time I do this it gives me "file can not be read". I was at the Mac store earlier today and we ran a disk utility and other tests and it does not seem to be my Mac. I have imported many photos and this is the first time I have experienced this message.
Do you have any other suggestions?
Open the destination panel on the right side; this seems to be a new bug(?) in LR 6.x
Thank you! After you sent that I went to the Mac HD at the top and saw it was not being sent anywhere…I changed it to pictures under Mac HD. Again, thank you ALL!
Well, it looks like the sub folder under the MacHD you have selected in the destination that does not have the proper permissions.
Please go to that folder using the Finder and then,
CMD+Click on the folder
Click on Get Info
Click on the Sharing & Permissions
Unlock the Pad lock
Check under the Name all User should have the Read & Write Access
Once you change the Permission, Apple the Enclosed item by click on tool icon at the bottom
Open Lightroom and try the import.