Compute .

You have both assumed that these are combinations - and you are most likely correct BUT

Couldn't those be vectors?

$$\begin{pmatrix}
16 \\
4
\end{pmatrix}
&-
\begin{pmatrix}
16 \\
12
\end{pmatrix}&=
\begin{pmatrix}
0 \\
-8
\end{pmatrix}$$

Another symbolism is:  ₁₆C₄ - ₁₆C₁₂

₁₆C₄ =  16!/(4!·12!)

₁₆C₁₂ =  16!/(12!·4!)

So, how much is  16!/(4!·12!)  -  16!/(12!·4!) ?

Notice something....that in combinatorics....

C(n, k)  is always the same thing as  C(n, n-k)

So if n = 16 and k = 4

C(16, 4) = C(16, 16-4) = C(16, 12)

And....if two things are equal, then, when we subtract one from another, the result is 0 !!