That depends exactly what you mean. If you mean what is the climactic point of the story (in a more strictly literary sense of 'climax') then that's might vary depending on how you interpret the story. It can also mean 'finishing point' or 'end'.
Here's climax defined:
- the decisive moment in a novel or play; "the deathbed scene is the climax of the play"
- culminate: end, especially to reach a final or climactic stage; "The meeting culminated in a tearful embrace"
So, to turn to this story, you can roughly break the story down into the following blocks.
1. Background on the Emperor and his greed.
2. Swindlers offer cloth to the Emperor and he orders it.
3. Old Minister goes to the swindlers and pretends to see the cloth.
4. Emperor dresses in suit when it is ready.
5. Emperor parades naked.
The climax of the story - the point to which the story as a whole builds up is undoubtedly number five, the parade when the Emperor walks down the street absolutely naked thinking he is wearing beautiful clothes. This too is more generally the 'climax' - the finishing point - as this is where Andersen stops telling the story. It is in both senses the climax of the tale.
Hope it helps!
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