I don't stand how this cross product work. Need explaining.

i j k i j k
2 2 -2 = 2 -2 - 2 -2 - 2 2
2 -2 2 -2 2 2 2 2 -2

I can't read your formatting.

Just recall that the cross product is just the determinant of the 3x3 array with i,j,k as the top row and the vector components as the other two rows.

google cross-product for many examples and discussions.