Cross-Cut
A cross-cut is typically the most aggressive response to a hane, leading immediately to fighting. It can also be used to make sabaki in the opponent's area of influence.
Follow up
The cross-cut produces an extremely urgent position, because there are four separate groups with only two liberties each. Therefore, tenuki next is very unlikely. Because the cross-cut typically leads to fighting, the follow-up usually must be chosen by reading and not by general principles. Two typical continuations are
Further reading