This question tests the concepts of parallelism and idioms. Correct idiom is 'Both X and Y, in which X and Y should be grammatically parallel.

(A) in the national economy growing most vigorously both through reducing taxes, especially taxes affecting large movements of capital, and by the elimination of
Not parallel, as gerund phrase 'through reducing taxes' is not parallel to noun phrase 'the elimination of...'

(B) in the national economy most vigorously growing both through the reduction of taxes, especially taxes affecting large movements of capital, and eliminating
Not parallel, as noun phrase 'reduction of taxes' is not parallel to gerund phrase 'eliminating...'

(C) that the national economy grows most vigorously through both reducing taxes, especially taxes affecting large movements of capital, and eliminating
Correct answer as simple gerund phrase reducing tax is parallel to eliminating...

(D) that the national economy grows most vigorously both through the reduction of taxes, especially taxes affecting large movements of capital, and also the elimination of
Incorrect idiom usage as Both X and also Y

(E) for the national economy to most vigorously grow both through reducing taxes, especially taxes affecting large movements of capital, and eliminating
Not parallel as 'through reducing tax' is starting with a preposition 'through' and eliminating is staring without the preposition