Help with alternate move on puzzle

Hi I’m totally new so please forgive me if this is obvious. I’m working through puzzles and I’m having difficulty with this one. I worked out that the correct move as black is M13 then M12 as white responds by taking L13 in the puzzle, however I can’t figure out why white doesn’t go for M12? I’ve played it through and can’t figure out how to make 2 eyes if white counters like this

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Black M13, followed by white M12 would allow black to Atari at N12, if white tried to connect at L13, then black captures at J13.
M13 M12 N12 L13 J13

This is not optimal play for white.


Thanks I missed that completely

Happy to help. If you practice counting liberties after each move, then these types of defenses will become almost automatic. Remember to count the liberties of different groups separately.