What is the correct cube action in these two positions for both black and white?

This lesson is about when to take a double when there is little contact left. In problem A white shouldn't have too much difficulty in getting the four checkers into the homeboard, and even if white does leave a shot it still has to be hit the very next roll. So the chances of getting that hit are low and it is a pass.

In position B white has more checkers to clear and whites board is much less strong. Black can hang around and wait for a chance to hit. Black also has a little bit better timing because there are four other checkers which black can move before having to break up the homeboard. This time it is a take.