The correct answer is the 3rd choice:
4/12 x 3/11
The explanation is that to start there are 12 total eggs of which 4 of them are boiled, so there is a 4/12 chance that the chef will get a hard boiled egg.
After removing one of the hard boiled eggs, there will be 3 hard boiled eggs remaining and one less total eggs (11).
To find the probability of getting a hard boiled egg both times, you multiply both probabilities together.