To screen women for colorectal cancer, the use of either colonoscopy

To screen women for colorectal cancer, the use of either colonoscopy or flexible sigmoidoscopy is acceptable although a recent study shows that this is the preferred method.

The above sentence has singular subject "the use" and hence "is" is correct verb.
A recent study shows that THIS is preferred method.
Two problems here.
- We don't have clear antecedent of "this". It could be colonoscopy or flexible sigmoidoscopy.
- THIS is a demonstrative pronoun and hence can't stand alone. It can be used as a noun modifier though. e.g. this method.

A. or flexible sigmoidoscopy is acceptable although a recent study shows that this
Incorrect for above reasons.
B. and flexible sigmoidoscopy is acceptable although a recent study shows that colonoscopy
Either- should be followed by Or (not - and).
C. or performing flexible sigmoidoscopy is acceptable although a recent study shows that the former
The use either X OR Y - is correct. Incorrect construction here : The use either X Or performing Y.
D. or flexible sigmoidoscopy is acceptable although a recent study shows that the former
Correct. Former stands for colonoscopy.
E. or flexible sigmoidoscopy is an acceptable method although a recent study shows that colonoscopy
The use of either X or Y is an acceptable method. - "the use" can't be a method !!

Hence, D