The solution is to play the kikashi at before living at . Why the kikashi at , and why here when there are other ways to live? The answers to these questions will be revealed at the end of the solution sequence.
Locally, is the only way to kill the lower left group. onwards is the only way out, and keep reading...
So the purpose of all these moves is to set up a ladder. (See Kyu Exercise 5 for an elaboration of these moves.) Does this ladder work?
The final result... is a double snapback on all the White stones. So that's the purpose of the first two Black moves marked !
(Note that ignoring in the original diagram to play in the lower left immediately doesn't help. This ladder still works then).
White, of course, should have read this out as well, and realized that in the first diagram is pointless...