i don't know if this is good or bad process, but I got this right by keying in on the word "solely"

Premise - Most theories are SOLELY (only) on theoretical grounds

Correct Answer (Additional Premise) - Objects posited for theoretical reasons only (SOLELY) should never be designated as real

Conclusion - Therefore this approach (designating as real based on the most explanatorily powerful theories) is flawed

Again, I don't know if this is good or bad process but I rationalized it as since most theories are solely theoretical, the subset of the most explanatorily powerful theories would contain some theories that solely exist on theoretical grounds. If this is true, and we accept answer B, then the conclusion would be flawed. I don't know if this was a reasonable assumption to make, but it got me to the right answer.

Would love to hear if anyone else felt the same way or if anyone could chime in on if this is a correct way to think about it #help

If A or B, then C:

A or B-> C

Think about what we know if it is A. If we know it is A, then we know it is C.

A-> C

What about if we know it is B? If we know B, then we know it is C.

B-> C

See how we have split the original conditional statement (If A or B, then C) into two separate statements. A-> C ; B-> C

It might work better to show this using a real life example which holds true.

Ex: If it's a cat or a dog, then it's a mammal. D or C -> M

From your intuition you would know when you see a cat, you know it's a mammal.

C-> M

And the same for a dog: D-> M

Once again we see that the logic still holds from the original statement, we are just able to break it into two statements because of the "OR"

I'm not familiar with your comment about not being able to have 2 SCs pointing to 1 NC, but it is certainly the case that "OR" presented in the sufficient condition can be split into two logical statements, with each component of the "OR" statement pointing to the same necessary condition.

Essentially the OR presents two independent elements, either of which are sufficient for the necessary condition, and because each are sufficient on their own to prove the necessary, each element can be represented individually as it's own statement to prove the necessary.

As opposed to AND statements in the sufficient condition, where the elements are dependent on each other co-existing to prove the necessary.

This is my first time responding to one of these but let me know if you have any questions, hopefully that was able to help some.