As mentioned, the reason you aren’t just finding the probability of peach candies is the phrase:
until he finds a peach one, at which point he stops.
Had this not been there, you could certainly treat it like Question 6, because a bijection exists even though we’re trying to transition from a uniform probability to a non-uniform one.
Basically, Question 6 has no restriction requiring the first 5 balls NOT be green, whereas Question 12 requires that the first two candy pieces are NOT peaches.