The diagram contains a complete set of domino tiles. Draw their borders to indicate where every tile is located.
There is only one position where the tile with [0,0] can be. [1,1] could be at several locations, but [2,2] also has only one possible position. Once we have drawn these tiles, the 1 in the top row can only be connected to the 1 below it; thus we now know where [1,1] is. The same argument holds for [0,2], because the 0 in the lower right corner can only be connected to the 2 to its left.
Now there are two possibilities to split the remainder into two tiles. A vertical split gives [0,2] and [1,1], but these tiles have both already been used. A horizontal split gives [0,1] and [1,2], and this is exactly what we need.