With the marked stones are captured but when Black captures back at , White cannot prevent Black from connecting at . The and approach moves come too late.
Karl Knechtel: (4 at marked stone) Also doesn't work, even though shutting off the corner like this is often a good idea in similar problems. a and b are miai to prevent an eye on that side, so Black only has the one eye in the corner.
Of course, with White first, taking the two stones kills easily in the same way. Starting with at also kills, of course.
Commentary - Akari is fooled because the key is not to save two stones that seem to be important for the group "structure", but to fall back and allow, even invite the capture - a move that to a beginner looks like a slip of the hand. I guess she never did get much stronger; too bad :(