X ~ Hypergeometric(N = 12, n = 4, D = 2).
Let Y be the random variable 'number of rotten eggs in second sample'.
Y ~ Hypergeometric(N = 8, n = 4, D = either 0, 1 or 2 depending on X).
What does "at best one of the first 4 was rotten" mean? Does it mean there was at least 1 rotten egg in the first four ....? Assuming it does, then you need to calculate .
But you will need to get clarification on this before the question can be done with certainty.