I arrived at answer E in about 15 seconds, surprisingly. Here’s what went through my head:
I saw the underlined comma in “missiles, induce” and the verb earlier on was “can affect the trajectory”
Immediately, I considered in my head that the answer is one of those -ING options like this:

Alternative #1:
“Displays of the aurora borealis, or “northern lights,” can heat the atmosphere over the arctic enough to affect the trajectories of ballistic missiles, inducing electric currents that can cause blackouts in some areas and corrosion in north-south pipelines.”

which can also be rewritten like this according to framework #3:

” Inducing electric currents that can cause blackouts in some areas and corrosion in north-south pipelines, displays of the aurora borealis, or “northern lights,” can heat the atmosphere over the arctic enough to affect the trajectories of ballistic missiles,.”

But I did not see any -ING versions of INDUCING in the answer choices as I quickly skimmed down the right side of the anwer choices.

Alternative #2:
The next alternative I considered was using the “and” conjunction. The first verb as we noted before was “can heat.” So naturally that should be followed like this:
“can affect X and induce Y”

Answer should be (D). It’s a bit tricky.

Once you see the word “assumptions” in the question, you should look back at the paragraph to see what claim is being made.

Here’s the claim:
“Stopping sales of video games –> less carpel tunnel syndrome”

Well, wait a minute. Look at the long chain of reasoning here:

There are 3 components:
1) Sales of video games -> 2) playing video games -> 3) carpel tunnel syndrome

More detailed, it looks like this:
1) Legislation that stops sales of video games –(causes)–> 2) playing video games –(causes)–> 3) carpel tunnel syndrome

Here’s the doctor’s claim: “Federal legislation that prohibits the sale of video games to minors would help curb this painful wrist condition among adolescents. ”

According to the reasoning chain above, getting rid of item #1: “sales of video games” through legislation will mean #2 and #3 will not exist.

Well, that assumes that #1: “sales of video games” will lead to #2: “playing video games”
How do we know that blocking sales of video games will necessarily lead to less playing of video games?

Well, the doctor assumes that by making it illegal for minors to purchase to purchase the games, the minors would have no other way to play the games. Well, common sense tells you that the minors can always get their parents/guardians to get the games for them. So the author assumes that this is not possible since they assume “most parents would refuse to purchase the games for their kids.”

With answer choice (D), that’s what you get:

“Most parents would refuse to purchase video games for their adolescent children.”

I still think answer (C) is an assumption in the 3 part assumption chain I mentioned above although it’s not an assumption of the doctor’s claim—small subtlety.

Here’s why:

In the 3 part reasoning chain:
1) Sales of video games -> 2) playing video games -> 3) carpel tunnel syndrome

the doctor’s claim is that getting rid of #1, you will no longer have #3.
Answer (D) describes the assumption between #1 and #2.
Answer (C) describes the assumption between #2 and #3.

Since the doctor’s claim begins further to the left on the reasoning chain (#1), the assumption must include #1. Although (C) seems like a legitimate assumption to me, it is an assumption related to a different part of the reasoning chain (#2 and #3).