The current solutions aren't the best, so I am going to try my best.
The quality of early pieces of blown glass excavated in Italy and Western Europe by far surpass those of pieces from the eastern Mediterranean, when regarded not only in terms of the variety of shapes represented, but also in terms of decorative techniques and functionality.
Here, the subject is "The quality." You know that "early pieces" is not the subject because it has the preposition "of" in front of it.
1st major split: do we use "that" or "those?"
Well, the subject is "The quality" which is singular. "that" is singular and "those" is plural, so we need "that."
Eliminate A and B.
2nd major split: "surpass" or "surpasses"
Well, since "that is singular" we need to use the singular "surpasses"
Eliminate C
There are two nice ways to choose E over D.
1. "that" refers to "the quality"
if you go with D, you would be saying that "The quality of early pieces of blown glass excavated in Italy and Western Europe far surpasses the quality of the eastern Mediterranean" We can't compare the quality of pieces with the quality of a geographical area"
if you go with E, you would be saying that "The quality of early pieces of blown glass excavated in Italy and Western Europe far surpasses that of pieces from the eastern Mediterranean." This makes sense, you are comparing the quality of pieces in Italy and Western Europe with the quality of the pieces from the eastern Mediterranean.
2. The parallelism of "not only... but also"
For these, what comes directly after "not only" must be parallel with what comes right after "but also"
In D, we say "with regard to not only the variety of shapes represented, but also in terms of decorative techniques and functionality."
"the variety of shapes" (noun) is not parallel with "in terms of" (non-noun), for my computer science friends, think of these as two different data types.
In E, we say "not only with regard to the variety of shapes represented, but also in terms of decorative techniques and functionality."
"not only with regard to the variety of shapes represented, but also in terms of decorative techniques and functionality."
"with regard to" and "in terms of" are parallel; look, they both start with prepositions ("with" and "in").
I hope I did an okay job hehe