Beyond 习惯 a general “framework” desired for 得's uses in “主语”“动词” 得是什么?, “主语” “动词” 得是鸟语，“主语” “动词” 得 “名词,” et cetera
@user58955 is correct. Example E to H are wrong usages of 得, they all should be 的 instead.

E. 她说的不是。 What she said is not. (This is a bad example. As you can see in the English translation, something is missing here.)
F. 不懂对方说的是什么。 Doesn't understand what the opponent says.
G. 你说的是鸟语。 What you said is lingua avis.
H. 你说的是什么？ What is it that you said?

The pattern is obvious.

Now let's take a look at example A to D:

A. 他跑得快。 He runs fast.
B. 他跑得很快。 He runs very fast.
C. 听得懂。 Listen get understood.
D. 办得了。 Do get done.

Notice in these 4 examples, 得 acts as a connecting device between the verb and the status or result of the verb. Also notice that the weight of the sentence is on the status or result, 快, 懂, or 了. This is how you use 得 to form complements. In a sense A, B are only slightly different from C, D in there specific purposes, but the major function is the same.

Example A and B -- You wouldn't call the English counterparts complements, do you? But remember I talked about the weights. If the weight is on the modifier, the modifier would be considered as a complement. If you want a non-complementary adverb, you need to use this form:

他飞快地跑。 He quickly runs.

Now the weight is on the verb 跑, and 飞快地 acts 状语 instead of 补语.
Example C and D -- There just isn't an English counterpart. This might be why it's confusing you and making you think it's special. It's not. You just have to think the Chinese way.