How to get the exact count.
In Diagram 16 Black has 1/3 point in the corner for the White ko stone in atari. White has 4 points. (It is somewhat arbitrary what you count, but they seem to be counting 4 of White's points.) Net result: -3 2/3 points for Black (3 2/3 points for White).
If Black plays from Diagram 15 instead of White, the net result is -3.
Since the moves are gote, the count for Diagram 15 is -3 1/3.
In Diagram 14 the net result is 0.
Since the moves Diagram 13 are gote, the count for Diagram 13 is -1 2/3.
The count for Diagram 11 is +5.
The original count is +1 2/3. Either gote gains 3 1/3. The swing between Diagram 11 and Diagram 15 is 6 2/3.

Edit:
Before someone else points it out,

in Diagram 16 is not exactly gote, since it gains 1/3 point and Black can also gain 1/3 point by taking the ko. Still, treating it as gote gives the right answer, as it is ambiguous.


in Diagram 12 is ambiguous, too, BTW. When the book was written go players did not understand about ambiguous plays.