Whenever you see a comparison word like "unlike," you want to ask yourself - what are we comparing? I like to think of this structure: "Unlike X, Y." Then I ask myself what the "X" and "Y" elements are, and if they're comparable.

In this sentence, we want to compare auto insurance to personal property coverage. Or perhaps auto insurance premiums to personal property coverage premiums. So let's see if that's what we're actually comparing here...

(A) Unlike auto insurance, the frequency of claims does not affect the premiums for personal property coverage
Unlike... insurance, the frequency... Can we compare insurance to frequency? Nope.

(B) Unlike with auto insurance, the frequency of claims do not affect the premiums for personal property coverage
Unlike with auto insurance, the frequency... We'd need another "with" for our X and Y elements to be comparable. And again, auto insurance and frequency aren't comparable anyway.

(C) Unlike the frequency of claims for auto insurance, the premiums for personal property coverage are not affected by the frequency of claims
Unlike the frequency... the premiums...? Nope, not comparable.

(D) Unlike the premiums for auto insurance, the premiums for personal property coverage are not affected by the frequency of claims
Unlike the premiums... the premiums... Looks good!

(E) Unlike with the premiums for auto insurance, the premiums for personal property coverage is not affected by the frequency of claims
Unlike with the premiums... the premiums... Once again, the "with" messed it up, and made these two not comparable.

So, regardless of anything else in the sentence, the only answer choice that compared two comparable elements was C.