TM4C129DNCPDT: TM4C129DNCPDT as frequency counter (12MHZ)

It is expected that the use of a, "CPP pin" - just as you noted - should work best.

Unstated is the "source" of this, "external, 12MHz clock." Usually best results flow from the shortest, most direct, signal introduction - and try to insure that (any other) HF signals do not run "near" (or especially in parallel) w/your external signal.

The MCU manual describes various, "Timer Configurations" - it is my experience that your, "experimentation - and observation of results - with several - yields the maximum learning."   (I'm no fan of  rushed, "Cookbook" (let's get this post "Off the List") response.)      (Never to state/suggest  - that such - occurs here...)

Update speed is likely to influence your, "Method of Attack" - you should note that a simple, Character-Type LCD/OLED, very well serves to Display your measurement's results.     And - if you are (both) "motivated & clever"  - may extend to an additional, "Frequency Channel" - and even,  "Several Channels of  Analog Voltage Measurement & Display" - as well.     (i.e. Makes the project/product - even MORE - desirable.)

Your identification of - and insertion - of a, "Higher Speed Capable/Accepting" Frequency Dividing IC (placed between your "external frequency Source" - and the MCU's CPP pin) - will  extend the frequency range of your project  - and likely will make it  more robust...  

Another point dawns - best that rather than,  "Grafting it into the earlier post" - it stands alone - to better, "capture your attention."    (maybe)

It is noted that,  "Many land here" - after,  "Crashing/Burning" - or when they have a specific,   "Interest du jour."    And - that may not always prove best - (both) for these posters - and for this forum.

Now you are specifically seeking  guidance so that a,  "12MHz, external clock, may be measured."      And - while perfectly valid - would you not be "better served" - by developing a method which proves,  "Far Broader in its frequency measuring capabilities?"     In addition - what if the pursuit of such "broadening" - applies to your "Learning" - as well as - any (sought)  "frequency measuring capability?" 

Does not the broader objective - register as (far) more valuable & appealing?      (while insuring the best possible outcome - for your 12MHz  (tightly restricted) measurement!)

Follows the various clock/timer modes - for this vendor's (smaller, '123) MCU)   (should be highly similar to your device - in this "Timer" regard)

It would appear that (either) "EDGE-based" Mode - best serves you.     But which - and when - and (even) WHY?

Experience teaches that your solving for (only) this (rather restricted)  "12 and only 12MHz"  measurement - will NOT produce,  "Full Learning!"     Would it not prove advantageous - to instead - extend your (high "accuracy) measurement  to encompass:  0.1Hz to beyond 100MHz?    

When might you switch from,  "One EDGE Method" - to the other?     And - can that "switching" be automated - so that the MCU performs the,  "Heavy Lifting?"

Might it be that your request - for  "CCP vs. GPIO" - would benefit - if (somewhat) extended?