Last two lines of the answer is simple and straight forward:
1. Point U and Point V form a vector UV = (3-2, 2-1, 1-[-1]) = (1, 1, 2)
2. an unit vector on the Y-axis is Z=(0, 1, 0).
Cross product of UV and Z is perpendicular to both UV and Z, hence it is the normal vector of the plane.
This normal vector is: (1,1,2) X (0,1,0) = (-2, 0, 1)