I think I can help!

sparkles3144 wrote:More adeptly handling responsibility than his predecessors were able to do, the new owner of the property rapidly increased the production rate of the land.

So the first thing to think about when reading this sentence is that we have to worry about modification. We need to make sure that we properly modify the "new owner." We also have a comparison here so we need to think about parallel structure when comparing.

Let's look at the answer choices.

sparkles3144 wrote: A.More adeptly handling responsibility than his predecessors were able to do
B.As he was more adept at handling responsibility than were his predecessors
C.Handling more responsibilities adeptly than his predecessors
D.More adept than his predecessors at handling responsibility
E.Since he handled responsibility in a manner more adept than that of his predecessors

First and foremost, if we want to start a sentence with a comparison and make it subordinate to the main clause of the sentence, as is the case here, we need to follow a specific structure:

"More x than y at z, ..."

If we know this then we can eliminate the other answer choices very quickly. If we don't know this, we can eliminate them in other ways.

Answer choice (E) introduces an unnecessary cause-and-effect relationship with "since." This is not appropriate so eliminate. We can eliminate answer choice (B) for the same reason with the use of "as."

Now we have three choices to work with. We can eliminate (C) pretty quickly as well. Namely, the adverb "adeptly" is not next to the thing that is should modify-"handling."

Once we get to this point, with two answer choices to choose from, I am always thinking about concise, clear language. I don't want to choose an answer choice that is cumbersome and more wordy. So even if I did not know about the rule mentioned above, I could still eliminate (A) and choose the correct answer just by choosing the answer choice that is more precise. The correct answer is has fewer words and conveys the same idea. Always choose the more precise option.

Does that make sense?

Let me know if I can make something more clear! Happy studying!