Q: My new iPad mini 4 won't sync with my macbook iTunes?

what version is your iTunes then? you probably need to update your iTunes

Don't worry about any iTunes version on the iPad itself.

iTunes 12.1.2 is insufficient to communicate to your iPad.  Your iPad, running iOS 9.xxx requires a more current iTunes on your computer.  (The current version is 12.3.2.)

iTunes 12.3.2 requires at least OS X 10.8.5 if you have a Mac (current is OS X 10.11.3).  If you have a Windows machine, you need at least Windows 7.

If you have the requisite operating system (unlikely), then update iTunes from:

http://www.apple.com/itunes/download

Otherwise, upgrade your operating system if you can.  If not, you will need a new computer.

I just realized you said you have a MacBook AIr.  If it's from late 2008 or newer, it can run El Capitan (OS X 10.11).  Get it from here:

Upgrade to OS X El Capitan - Apple Support

Then go to the Mac's App Store and update all software.  You will then have the latest iTunes.

Excellent.

Yosemite is capable of running iTunes 12.3.2 if you wish to do that.  Otherwise, you could upgrade to El Capitan.  It's your choice.