By sucking sap from the young twigs of the hemlock tree, tree growth is retarded by the woolly adelgid, causing needles to change color from deep green to grayish green and to drop prematurely.

The sentence begins with a modifier. So, when we get to the comma, we should stop and ask the question that the modifier raises. Here the question is, "Who or what sucks sap from young twigs?"
The part immediately following the comma should answer our question in a logical manner.

A. tree growth is retarded by the woolly adelgid, causing needles to change color from deep green to grayish green and to drop
Tree growth sucks sap from young twigs?
Makes no sense. Eliminate A.


B. tree growth is retarded by the woolly adelgid, and this causes the color of needles to change from deep green to grayish green, and their dropping
Tree growth sucks sap from young twigs?
Makes no sense. Eliminate B.

C. the woolly adelgid retards tree growth, which causes needles to change color from deep green to grayish green, and dropping
The woolly adelgid sucks sap from young twigs? Makes sense - keep C for now.

D. the woolly adelgid retards tree growth, causing needles to change color from deep green to grayish green and to drop
The woolly adelgid sucks sap from young twigs? Makes sense - keep D for now.

E. the woolly adelgid retards tree growth, and this causes the color of needles to change from deep green to grayish green, and the their dropping
The woolly adelgid sucks sap from young twigs? Makes sense - keep E for now.

Now, compare C, D and E for other issues.

Note: The retarded tree growth causes 2 things:
1) needles change color
2) needles drop prematurely.

We need parallelism here.

C. the woolly adelgid retards tree growth, which causes needles to change color from deep green to grayish green, and dropping
Not parallel. Eliminate.

D. the woolly adelgid retards tree growth, causing needles to change color from deep green to grayish green and to drop
Parallel. Keep.

E. the woolly adelgid retards tree growth, and this causes the color of needles to change from deep green to grayish green, and the their dropping
Not parallel. Eliminate.

Answer = D

Cheers,
Brent

Just to confirm , In option C which doe not have any noun to refer.
That's right. We don't know what is dropping.

In option E this may refer to the woolly adelgid or tree growth
Yes, this is another reason to eliminate E

Cheers,
Brent