Don't use thickness to make territory

Black's direction is bad  

The advice is not to play short extensions such as here, which gains only a handful of points. Black's position to the right is very thick - it can only give its full strategic value if Black uses it in a dynamic, fighting plan.

Correct direction  

Black should play from the other side, with here. Then looks like a mistake^[1]: to attack is good.

White should play at or a (see problem 45 in Strategic Concepts of Go), staying away from thickness herself.

In any case the territory on the upper side is important mostly as a base for White's group, not for the few points it represents.

The fundamental ideas here for Black's use of thickness are thickness should be used for fighting and Black will take profit elsewhere, in this case in the left corner.

Analysis  

Another useful way to analyse is to say that Black already has some points such as the circled ones because of his outside strength here. A black play at a is overconcentrated because it is only claiming points to which Black already has a right.

Shimari cum extension  

Perhaps Black's ideal play is , combining shimari and extension. The 5 space extension is good, as it does not leave White's invasion, , room for a two space extension after .

White's play?  

As for White's play, I think that each of a - e is worth considering.

Charles Here White c can be considered normal, to seek quick life. If White d, the intention would be to play the nadare (which would go into a small nadare line, assuming strong players). White e is a special technique, probably dependent on some ladder(s).