Thanks for looking up and sharing the rule with all of us. It may help you make sense of it if you realize that ע, ה and ח are so weak that if you have 'a, ha, and kha, and precede them with ha, it will run together and the second syllable (the weak syllable) will blend into the first and be lost. But if you have ה + segol in front of it, it allows you to differentiate and hear both syllables.
The answer it looks for is "The smoke comes out of the ground". Why would this not be written as "העשן בא מן הקרקע"?
I thought that the emphasis would have been more like "The smoke gets out from under the ground" which was not acceptable as an answer (probably for a good reason which is why I ask here).