I guess you figured the part that the main sentence has a Subject-Verb agreement error. Here's my break-down of the original sentence:
In the next few weeks: prepositional phrase
both the Federal....privacy: main clause
Federal Trade Commission & Commerce Department: Compound Subject
is: main verb (the error lies here, the verb 'is' ought to be plural to agree with the compound subject)

Based on the S-V agreement error, eliminate A.

B. the Federal Trade Commission and the Commerce Department are both planning to release independent, and possibly conflicting,
Incorrect. 'are both planning' is different from 'both...are planning'. The former suggests that the subject(s) plan to do more than one thing versus the latter, which, means that both the subjects (FTC & CD) have plans to do the same thing.

C. the Federal Trade Commission and the Commerce Department both are planning to release independent, but possibly conflicting,'bo
Seems awkwardly constructed in the way 'both' is placed. You don't say "Jack and Jill both went up the hill" it should instead be "Both Jack and Jill went up the hill"

D. both the Federal Trade Commission as well as the Commerce Department are planning to release independent, and possibly conflicting,
Incorrect idiomatic usage. The correct usage is "both X and Y" and not "both X as well as Y"

E. both the Federal Trade Commission and the Commerce Department are planning to release independent, and possibly conflicting,
Is the correct choice because it fixes the S-V error in the question stem and uses the correct idiomatic expression "both X and Y"

any expert please?

Experts Please help

Two things before I put my analysis
correct idiom is,
1. Both X and Y
2. "AND" makes a compound/plural subject, so verb should be in plural form.

A. both the Federal Trade Commission and the Commerce Department is planning to release independent, and possibly conflicting,
both X and Y is = wrong
B. the Federal Trade Commission and the Commerce Department are both planning to release independent, and possibly conflicting,
X and Y are both = wrong
C. the Federal Trade Commission and the Commerce Department both are planning to release independent, but possibly conflicting,
X and Y both are = wrong
D. both the Federal Trade Commission as well as the Commerce Department are planning to release independent, and possibly conflicting,
both X as well as Y are = wrong, as well as does not make compound subject, ONLY AND DOES
E. both the Federal Trade Commission and the Commerce Department are planning to release independent, and possibly conflicting,
both X and Y are = correct !

gtestprep wrote:I guess you figured the part that the main sentence has a Subject-Verb agreement error. Here's my break-down of the original sentence:
In the next few weeks: prepositional phrase
both the Federal....privacy: main clause
Federal Trade Commission & Commerce Department: Compound Subject
is: main verb (the error lies here, the verb 'is' ought to be plural to agree with the compound subject)

Based on the S-V agreement error, eliminate A.

B. the Federal Trade Commission and the Commerce Department are both planning to release independent, and possibly conflicting,
Incorrect. 'are both planning' is different from 'both...are planning'. The former suggests that the subject(s) plan to do more than one thing versus the latter, which, means that both the subjects (FTC & CD) have plans to do the same thing.

C. the Federal Trade Commission and the Commerce Department both are planning to release independent, but possibly conflicting,'bo
Seems awkwardly constructed in the way 'both' is placed. You don't say "Jack and Jill both went up the hill" it should instead be "Both Jack and Jill went up the hill"

D. both the Federal Trade Commission as well as the Commerce Department are planning to release independent, and possibly conflicting,
Incorrect idiomatic usage. The correct usage is "both X and Y" and not "both X as well as Y"

E. both the Federal Trade Commission and the Commerce Department are planning to release independent, and possibly conflicting,
Is the correct choice because it fixes the S-V error in the question stem and uses the correct idiomatic expression "both X and Y"

You nailed it..

even i chose C option...

but with the eg you given in case of C option, it is fine with me that C is incorrect...!

Thanks...

The problem is that "both" can be a pronoun or an adjective or a conjunction. As a pronoun, it can stand before a verb as the subject of the sentence: Both are good; it is this usage which makes C confusing and undesirable, because it looks like a comma splice.