Can Ubuntu 12.04 be upgraded to 14.04 instead of 16.04?

You can check the release you'll get with do-release-upgrade by adding the -c flag like so:

do-release-upgrade -c

As far I understand, there is not yet an upgrade possibility for upgrading 12.04 LTS to 16.04 without going step by step (i.e. to 14.04 on the first run), so do-release-upgrade can be expected to do exactly what you want.

I tested this just now.

$ lsb_release -a 
No LSB modules are available. 
Distributor ID: Ubuntu
Description:    Ubuntu 12.04.5 LTS 
Release:    12.04 Codename: precise

Then:

$ sudo do-release-upgrade
Checking for a new Ubuntu release 
Get:1 Upgrade tool signature [198 B]         
et:2 Upgrade tool [1,156 kB]                                         
Fetched 1,156 kB in 0s (0 B/s)                                        

authenticate 'trusty.tar.gz' against 'trusty.tar.gz.gpg'  extracting 'trusty.tar.gz'

You cannot currently upgrade directly from 12.04 to 16.04; you have to upgrade to 14.04 in-between. So simply running the following will upgrade you to 14.04:

sudo do-release-upgrade

Then if you don't want to upgrade again to 16.04, just stop there rather than performing another upgrade.

Or (for the GUI way - the relevant program is also known as the Software Updater and can be searched and found in the GUI under that name):

update-manager

For this though once you are completely up-to-date with all the latest updates it will show you an Upgrade... button which will allow you to upgrade to 14.04.