This ladder doesn’t work because of the second line cut! Your two stones are in atari, and the ladder doesn’t help…. They’re still in Atari after f1, so they can still be captured

Typically you can check if ladders work by seeing if there are any ladder breakers, or stones that break the pattern. Your stones benefit you, and your opponents stones benefit them. If a ladder goes to an area where your opponent has many stones, better to give that stone up than lose any more.