If the iTunes neither recognizes the device you connect to your Mac, nor show the icon for your device, it may be caused by the following reasons.
Before we get down to the specific reasons, you need to know where to locate your devices. And one thing you need to keep in mind is that where to find you device depends on the version of your iTunes.
For iTunes 12:
Locate your device by tapping on the device's icon in the top left corner of the iTunes window.
For iTunes 11:
Find your device by hitting on the button showing your device's name in the top right corner of the iTunes window. If you're in the iTunes Store, hit the Library button in the top right corner first. If you don't see your device, select View > Hide Sidebar.
Reason 1: The device isn’t turned on.
Make sure you have turned on your device before you plug it into your computer and you can get to the home screen. If you forgot your password tragically, the only way is to erase all the content presently on your iPhone, iPad or iPod Touch by using “Recovery Mode”.
Reason 2: Your Mac does not support your device.
You need to make sure your device is compatible with the OS system you are running. For example, if you are trying to sync your iPhone 6 Plus on your Mac, make sure your have OS X v10.6.8 or later running.
Reason 3: You didn’t tap “Trust this Computer.”
After you get your iPhone, iPad or iPod Touch connected to your computer, there will be an alert popped up on your iPhone, iPad or iPod Touch asking to trust the computer through which you would like to restore or sync with iTunes.
Reason 4: The iTunes is not the latest version.
Make sure you have got the latest version of iTunes, or at least make sure the device you are connecting to computer is compatible with current version of your iTunes, for example, you need to run the iTunes 11 or above for your iPhone 6 Plus.
Reason 5: The Cable is dirty or broken or just does not work.
Try cleaning your USB cable, or simply change for another USB cable or the USB port.
If all the solutions above don’t work for you, try rebooting your device or your computer. If this does not work either, contact Apple for support.