Looking at KS mock 3 109-114 In the problem it states that she wants to hedge for 90 days. Question asks which position is best with 1 month 3 month and 6 month short call options. The answer was the 1 month because the quantity matched. How does one know to go for quantity over time? Also said the future price today is xx. But when it did the calculation it discounted the today price. Why?

That would give you a perfect delta hedge.

#of stock/Delta

Only option 1 seems like the best option out of three.