Let's consider the picture above.
For each row we can pick exactly 4 different groups of 3 consecutive boxes.
In the same manner, for each column we can select 4 different groups of 3 consecutive boxes.
Therefore, snce we are required the maximum number of 3x3 squares of the chessboard,
we need to combine our combinations:
4 * 4 = 16
Answer is D.
Hope is clear.
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Can you elaborate a little bit. I do not know how you get the 4*4

I believe an image may better explain it:

"For each row we can pick exactly 4 different groups of 3 consecutive boxes.
In the same manner, for each column we can select 4 different groups of 3 consecutive boxes."

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Grouping the top 3 rows, among the 6 columns, adjacent 3 columns can be selected in 4 ways which can give 3x3 box. Similarly when done for columns, we get 4 ways for 3x3 box. So, total number can be 4*4 = 16 boxes.
My explanation might be not very clear, but thanks to other user who took sometime to explain with images.

Is there a way to write this in combinatorics???

the easiest IMO, it's a simple counting problem 4x4 of three-square figure in the upper left corner
the figure may move 4 times leftward and 4 times downward, in total 16 times