The plan calls for deep cuts in domestic and military

Hello, my friend. I'm happy to help with this.

The first issue is parallelism --- consider the prompt:
The plan calls for deep cuts in domestic and military spending, gradually increasing the federal gasoline tax by 15-cents-a-gallon, elimination of popular tax breaks and incentives and increasing the retirement age for social security.
Those four underlined terms are in parallel, and need to have the same grammatical structure. What we have is
(a) deep cuts (noun)
(b) increasing (gerund)
(c) elimination (noun)
(d) increasing (gerund)
On GMAT SC, this isn't going to fly. This is not correct parallel structure. (A) is definitely wrong.

The words "deep cuts" are in the pre-underlined part, so since that can't change, we need the other elements to be ordinary nouns.

(B) has [noun], [gerund], [noun] = wrong
(C) has the awkward "___ and ___ along with ____" --- this structure is never correct on the GMAT SC. Wrong

Both (D) and (E) have all nouns, so they get the basics of the parallelism correct.

(D) does something very interesting --- it inserts that funny word "through" --- first of all, this radically changes the meaning of the sentence. Instead of four things in parallel, we have [thing #1]"through"[the other three things in parallel]. That's a different logical arrangement, which should immediate get us suspicious. Furthermore, think about the context ---- "deep cuts in domestic and military spending, through a gradual 15-cents-a-gallon increase in the federal gasoline tax ...." --- the tax increase is an increase on the revenue side --- it's not a cut on the spending side. Yes, it makes sense that if the government is cutting expenses and trying to balance the budget, it might also, as an additional and separate move, increase revenue through something like a gas tax. The important thing to recognize is --- the gas tax, on the revenue side, can not be a part of the deep cuts, on the spending side --- it has to be something in addition to the cuts, not a part of the cuts. That's why the "through" construction makes no sense, and (D) is wrong.

This leaves only (E) as the correct answer.

Typically, the GMAT strongly favors turning action words into verbs --- "eliminating X" instead of "elimination of X", "increasing X" instead of "an increase in X" --- in the vast majority of cases on the real GMAT, the correct answer will involve the verb form, and the noun forms of action words will only appear in the incorrect choices. That's a guideline, not a hard-and-fast rule. The fact that this question hinges on turning a few action words into their noun form does make me a little suspicious of the quality of this particular source.

Let me know if you have any further questions.

Mike