A Mainer Expression

Question

+--------------+--------------+--------------+--------------+  
|  Box         |   Day        |   Files      |   Means      |  
+--------------+--------------+--------------+--------------+  
|  Love        |   Span       |   Objective  |   Pad        |  
+--------------+--------------+--------------+--------------+  
|  Tenacious   |   Sharp      |   Wave       |   Ray        |  
+--------------+--------------+--------------+--------------+  
|  Special     |   Section    |   Men        |   Pop        |  
+==============+==============+==============+==============+  
|  Step        |   Bit        |   Tone       |   Oz         |  
+--------------+--------------+--------------+--------------+  
|  Prop        |   Ground     |   Absolute   |   Mile       |  
+--------------+--------------+--------------+--------------+  
|  Hateful     |   Coke       |   Ball       |   Spirit     |  
+--------------+--------------+--------------+--------------+  
|  Beg         |   Patient    |   Face       |   Some       |  
+--------------+--------------+--------------+--------------+ 

What do they say in Maine?

Answer 1

Nice puzzle! In Maine, they say:

SUGAR MILK!

Why? Well, first notice that what we have here are:

Two connecting walls.

Furthermore, it turns out that:

In the topmost wall the 4 connecting groups are all individual letters, while in the bottom-most wall the 4 connecting groups are individual numbers.

Like so:

WALL 1

Group 1: X
X-box (games console)
X-Files (TV show)
X-Men (Marvel franchise)
X-Ray (medical imaging)

Group 2: K
K-LOVE (Christian radio station)
Special K (cereal)
k-means (a statistical test)
K-Pop (music genre)

Group 3: C
C-Span (TV channel)
Objective-C (programming language)
C Sharp (programming language)
C-Section (medical procedure)

Group 4: D
Tenacious D (comedy music duo)
D-Wave (Canadian quantum computing company)
D-Pad (games console controller)
D-Day (Normandy landings, WW2)

WALL 2

Group 1: 2
Two Step (dance)
Two Tone (music genre)
Two-Face (Batman baddie)
Two-Spirit (Native American term)

Group 2: 1
Propone ("To bring before a jury or judge")
Begone
Ozone (atmospheric layer)
Someone

Group 3: 0
Coke Zero (soft drink)
Ground Zero (disaster epicentre)
Patient Zero (first case in an epidemic)
Absolute Zero (coldest possible temperature)

Group 4: 8
Hateful 8 (movie)
8-Bit (computer architecture)
8-Ball (black pool ball)
8-Mile (movie)

Next, notice that:

The positions of the groups as I have numbered them above correspond exactly across the two grids - i.e. the positions corresponding to elements in Group 1 (X) in Wall 1 exactly match those corresponding to elements in Group 1 (2) in Wall 2, and similarly for Groups numbered 2, 3 and 4:

From this, we should infer that:

We can pair X with 2, K with 1, C with 0 and D with 8. In other words, we can arrange these ordered pairs to form XKCD 2108 - and what else could this be but a reference to a certain well known web comic, where instalment #2108 is this?

If we look at Maine specifically (the upper-rightmost state in the image) we see that:

People from Maine would call their carbonated beverages "SUGAR MILK"!