Final solution at one place:

Important: The purpose of this post (and all the other posts by me) is to give a complete solution to all GMAT-Prep Verbal questions at one place. Sometimes students have to wade through dozens of posts to get to the final answer. My posts will give one complete and crisp solution required to arrive at the correct answer by eliminating the wrong one. Some of the content in these posts may have been taken from various other sources (discussion forums).

The majority of scientists believe that to reduce and stabilize atmospheric concentrations of carbon dioxide, emissions must be cut at the source by fossil fuels that are burned more efficiently and, in some cases, by alternatives such as hydrogen fuel cells that can replace fossil fuels altogether.
(A) fossil fuels that are burned more efficiently and, in some cases, by alternatives such as hydrogen fuel cells that can replace fossil fuels altogether
(B) fossil fuels that are burned more efficiently and, in some cases, those that are replaced altogether with alternatives such as hydrogen fuel cells
(C) burning fossil fuels more efficiently and, in some cases, by replacing fossil fuels altogether with alternatives such as hydrogen fuel cells
(D) more efficiency in the burning of fossil fuels and, in some cases, by alternatives such as hydrogen fuel cells that can replace fossil fuels altogether
(E) the more efficient burning of fossil fuels and, in some cases, by fossil fuels that are replaced altogether with alternatives such as hydrogen fuel cells

This sentence needs a common construction: 'by + verb-ing'. 'By' is used when you describe the method used to accomplish (HOW) something - exactly what is done in this sentence. The sentence is explaining how the states are going to accomplish the stated goal.

If we say:

You should study daily. By doing so, you will improve consistently.

Or

One can't become smarter by facing the same challenges every day.

A and B are wrong because emissions can't be cut by fossil fuels ... rather they can be cut by more efficient burning of fossil fuels.

D is not parallel; 'by more efficiency' is not parallel to 'alternatives (fuels)'.

E is not parallel; 'the more efficient burning' is not parallel to 'fossil fuels'.

C is perfectly parallel ... by burning || by replacing.

C: correct.