The reason for selecting option 2, "how old I was," is that it maintains the correct word order and tense when transforming a direct question into reported speech. In reported speech, we generally shift the tense of the direct question back one step, and the word order is typically "subject + verb." Therefore, the correct structure is "Venkey asked me how old I was." Options 1, 3, and 4 do not follow the correct word order and verb tense for reported speech in this context.