Hi 1997! Great question
What Robert's hypothetical shows is that answer choice (D) only works as a substitute for the last rule when the sufficient condition occurs (H is a nominee for councillor), but not when the sufficient condition does not occur (H is not a nominee for councillor).
This is a bit different than saying that taking the contrapositive of answer choice (D) gives us a different result than the rule we're substituting for. Taking the contrapositive would mean "If K is not a nominee, then H is not a nominee for councillor." What Robert is referring to is taking a look at what happens if the sufficient condition does not happen.
Robert's hypothetical shows us that answer choice (D) does not always prevent K from being a nominee for councillor, which is the rule we want to substitute for. From answer choice (D), we know that if H is a nominee for councillor, then K cannot be a nominee (meaning K can't be a nominee for councillor or mayor). But if H is not a nominee for councillor, what do we know about K? We actually don't know anything about K then, and Robert's hypothetical shows a situation that is consistent with all of the rules and the rule proposed by answer choice (D) but violates the last rule that we're trying to substitute for. For a rule substitution question, we want to make sure that the new rule has the same effects as the old rule, but this hypothetical shows us that this isn't the case for answer choice (D).
I hope this helps, and let me know if you have any other questions!