Common shape in a 4-4 joseki

1

When white extends up, black used to respond at A, but…

2

White can cut at A to fight or simply play B to take the corner. Both variations are good for white.

3

So now people will exchange this hane first.

4

If white cuts, black can sacrifice the stones to gain thickness. This is good for black.

5

If white hanes back, black can just connect, and the white stone on the left side is getting alone.

6

If white pushes up like before, now the corner and the side become miai

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