Generally speaking the posts should be burried 1/3 deep. For a 2m fence you should use 3m posts. 2.4m posts are really for 1.8m fences.
In reality it depends on the ground conditions. Sometimes you can get away with less than 1/3, and sometimes you need more, but I would not expect 40cm to hold a 2m high fence upright for very long. You'll need double that.
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