Official Explanation Magoosh:
While it's not directly relevant to solving the question, you may find this blog on "means of" vs. "means to" helpful.
Split #1a: the "missing verb" mistake. The subject is the gerund phrase beginning with the gerund "extracting" has no verb in choices (A) & (B).
Split #1b: verb tense. Choices (C) & (D) & (E) provide a proper verb, although the present progressive "is making" in (C) is inappropriate — there is no contextual reason to emphasize simultaneity. Only (D) & (E) contain the correct verb "makes".
Split #2: phrasing. The participial "using" is awkward because there is no explicit noun it modifies: in this context, the phrase "by means of" is far superior. BTW, the phrase "by means of using" in (C) is an abomination — awkward, repetitive, and incorrect.
Split #3: preposition phrase vs. clause. The prepositional phrase beginning with "with a vast amount…" is also awkward — it is meant to describe an action, a process, that takes place within the Hall-Héroult process. A preposition such as "with" is not appropriate for describing an action contained within something else. We need a full subordinate clause, with its own subject + verb — this is precisely what the construction "in which a vast amount…" supplies. This is the problem with (A) & (E).
For all of these reasons, (D) is the strongest answer.