pieces that share the same row are: $$$\newline$$$ (1,1) and (1,2) $$$\newline$$$ (2,1) and (2,4) $$$\newline$$$ (3,2) and (3,3) $$$\newline$$$ (4,2) and (4,3) $$$\newline$$$ pieces that share the same column are: $$$\newline$$$ (1,1) and (2,1) $$$\newline$$$ (1,2) and (3,2) $$$\newline$$$ (1,2) and (4,2) $$$\newline$$$ (3,2) and (4,2) $$$\newline$$$ (3,3) and (4,3) $$$\newline$$$ The total is 9. $$$\newline$$$ I think you made a little mistake by not counting the 3 possible combinations in column 2.

You are calculating pairs of chocolates that share the same row and column. In second example:

1st row has 1 pair: {(1,1) , (1,2)}

2nd row has 3 pairs: {(2, 1), (2, 3)}, {(2, 1), (2, 4)} , {(2,3), (2,4)}

3rd row has 1 pair: {(3, 3), (3, 4)}

4th row has no pairs because it has only 1 element;

All columns have only 1 pair each:

1st: {(1, 1), (2, 1)} 2nd: {(1, 2), (4, 2)} 3rd: {(2, 3), (3, 3)} 4th: {(2, 4), (3, 4)}

Counting all pairs we get: sol = 1 + 3 + 1 + 0 + 1 + 1 + 1 + 1 = 9

In case you don't know, there is also a formula for calculating pairs in single column/row