Following is a response from DHS Research & Data Analysis Director, Tom Pullum:
Users are asked to specify the table they are trying to match. You are apparently referring to table 10.8.
The symptom of ARI that DHS surveys ask about is difficulty breathing that involves "the chest". In terms of h31c, these are categories 1 ("chest only") and 3 (" both [chest and nose]") . The denominator for table 10.8 is children in the KR file for whom h31c is 1 or 3. You will get the frequencies in the last column of table 10.8, for region, with this Stata command:
tab v024 if h31c==1 | h31c==3 [iweight=v005/1000000]
In the interpretation of the table, I would emphasize that it describes the prevalence of this symptom of ARI, but not a diagnosis of ARI.