Final answer:
While the story might have events that mention the months of July and August, without more specific information from the text, the exact date the boys climbed Kloochman Rock cannot be determined.
Step-by-step explanation:
Based on the text excerpts provided, it appears that the story in question might cover multiple time frames or events on different days, as specific months and years are not explicitly mentioned in the segments provided. However, it is possible to infer that some of the events might have taken place in July based on the contextual clues from the narrative 'July under the lee of the diamond mountain....' Additionally, the mention of August in '... the little boys taking off their shoes and stockings. At first August refused to be comforted...' could imply activities or elements of the plot occurring in August. Nonetheless, without direct quotes or more specific details from the text regarding the climbing of Kloochman Rock, determining an exact month and year is not feasible.