Double hane example 1

Double hane on the 3rd line  

is a powerful play as it shuts White into the corner. White cannot counter :

The counter fails  

If White resists by capturing a stone, Black captures the marked stones and kills the corner as well. As in the diagram above is such a powerful play, White has actually made a mistake before and should have extended to above himself.

Defend  

If White defends at , (or a or b) connects and gains major influence towars centre and side. The idea was not to kill White in the first place. That's just a punishment if white tries to get too fancy. The idea of this maneuver is to seal white into the corner.

Cut and defend  

Of course, White can still play backtrack to here. Now the situation depends on the ladder at a. Black has alternatives at b (if there are friends down the side) and c (a loose ladder follow-up to expand the influence.

Just extend  

The double hane compares to this mere extension. White can continue at a, crawling from behind, or just tenuki. Black will play this if there is trouble in the double hane, especially in the "cut and defend" variation.