Option(E) is correct
Franklin Roosevelt did two things to set the United States on a course to propel itself out of the depression: (1) confronting a devastated economy (2) improving the morale of the demoralized country. Both these two actions and the list of steps taken to accomplish them need to be parallel. Since the first action (followed with its list of steps) is introduced with by the second action (followed with its list of steps) should also be introduced with by.
The correct insertion into the underlined portion of the sentence should begin with and launching massive since this is the third and final step in the list of actions taken to confront a devastated economy.
The correct sentence should read: By confronting a devastated economy through {list of actions in parallel}, and by improving the morale of a demoralized nation through {list of actions in parallel}
The correct sentence should read: By confronting a devastated economy through actions such as creating the Federal Deposit Insurance Corporation, opening the Securities and Exchange Commission, suspending the gold standard, and launching massive public works programs, and by improving the morale of a demoralized nation through his fireside chats, First Inaugural address, and other motivational speeches, Franklin Roosevelt both...
A. the sentence is not parallel (i.e., the phrase by confronting x through y...and improving m through n is not parallel); the word and should be inserted before the word launching since launching describes the third and final step in the first series of actions Franklin Roosevelt took
B. the sentence is not parallel (i.e., the phrase by confronting x through y...and improving m through n is not parallel)
C. this sentence carries a pernicious distortion of meaning as the phrase a demoralized nation through is replaced with the phrase a nation demoralized through, which distorts the sentence to mean that Roosevelt's speeches were the source of the nation's demoralization
D. the phrase through the launch of takes away the parallelism of the list of items taken to accomplish the first action (i.e., the phrase creating..., opening..., and through the launch is not parallel)
E. the sentence is parallel (i.e., the phrase by confronting x through y...and by improving m through n is parallel)