In Puzzle #6, Blue has several ways to fail.
Blue can’t make territory with 3 on the right. Red shuts that down with 4, and then locks Blue in with 6.
Blue can’t escape with 3 on the left. Red shuts the door with 4, and then blocks Blue from making territory with 6.
So what will work? Blue 3, shown here. It prevents Red from playing there. Now if Red makes any move other than 4 or A, Blue plays at A and makes territory immediately.
Note that although Blue escapes with 5 and 1 is safe from becoming a prisoner, Red can follow up with 6 at B and take a total of 15^2 = 225 points, so this isn’t a very good outcome for Blue. He had better ways to invade — the next puzzle will look at that.