Q: how do I download a picture from my mac to iPhone

If you have your Mac Apple menu > System Preferences > iCloud > Photos Options > iCloud Photo Library turned on then all of the pictures in Photos should automatically upload from your Mac to https://www.icloud.com/ and if you have your iPhone Settings > iCloud > Photos > iCloud Photo Library turned on they should then automatically download to your iPhone. Check to see if your Mac and iPhone have iCloud Photo Library turned on.

Sorry -- I just woke up and noticed that your post said you are running Mountain Lion on your Mac. With that, it isn't possible for you to turn on iCloud Photo Library on the Mac. You can manually upload photos from your Mac to the Photos app at https://www.icloud.com/ and then they will automatically download to your phone. That procedure is described in the Windows section of http://www.timeboxapp.com/blog/2015/4/27/enabling-icloud-photo-library-and-itune s-sync

There isn't a way to transfer via USB cable directly from one iPhone to another iPhone. email might be the easiest but another method is via AirDrop: Share content with AirDrop from your iPhone, iPad, or iPod touch - Apple Support or via iCloud Photo Sharing iCloud Photo Sharing FAQ - Apple Support