The vector v is given by:

However, when he uses the transformation, he applies the following vector for B:

In another words, the vector v is a translation of 3 units to the right and 3 units down, however when he applies the translation to the point B, he uses a translation of 4 units right and 2 units down.
Also, for point A:

To the point A, he uses a translation of 3 units right and 2 units down.