This is a standard double shortage of liberties problem. The captured Black stones form a bent-four living shape, so White lives.
The move here has the same aim as that of the solution, but
can connect and give up the two Black stones. After
, White has only one eye.
Enlarging the eye space at here is also a failure. After
, White ends up in a standard L-group dead shape.
This diagram is only for reference. The jump at here is a tesuji that is often seen in such a corner pattern, and in this case allows White to live as well. But in this problem, it is inferior to capturing the four Black stones.