"Out of the frying pan into the fire" means:

In the given question, the phrase ‘out of the skillet into the fire’ is employed to ask a situation where someone is forced to be in one difficult situation and is soon in another difficulty, even greater than the previous.
Keeping this meaning in mind, allow us to study the choices given within the question, one by one.
Option ‘A’, it is easy, is inaccurate because the given phrase talks about difficulty, not ease.
Option ‘B’, from one kitchen to a different, is inaccurate as if the word pan is employed, it's not literal respect to the kitchen.
Option ‘D’, from one place to a different, is inaccurate because it has no relevancy only moving from place to put.
Hence, the proper answer is option ‘C’, from one trouble to a different bigger trouble, is that the correct answer because it perfectly describes the case that we discussed.