How many balls can a pitcher throw in one inning without the other team scoring?

Number of Balls a Pitcher Can Throw in One Inning

On the 16th bal, the original player that was "walked" will cross the home plate. So 15 balls are the most you can throw in one inning.

23 - If the pitcher picks-off 2 of the runners, he can then walk two more batters before pithing 3 balls to the final batter.

I think that it could be 24. If the pitcher picks off 2 of the runners after loading the bases as you say. The pitcher walks two more hitters to load the bases. Then the pitcher throws 4 balls to the next hitter but the runner from third fails to touch home plate and on appeal, that runner is called out to end the inning.