How will the right answer fit in terms of support and conclusion?

Only the right answer will add support for the conclusion in the passage.

Highlight the main conclusion in the passage, if there is one:

no new taxes supporting the library system should be approved unless the library hours are changed to better suit taxpayers and their families.

Politician: [BACKGROUND]. Hence, [SUPPORT]. Therefore, [CONCLUSION].

The right answer is a principle, so it’s going to echo the judgment in the conclusion pretty much exactly. You can eliminate any answer that doesn’t say something equivalent to “no new taxes…should be approved unless…”

(A) …should be made as convenient as possible…

That’s the wrong recommendation. We’re justifying not approving new taxes, we’re not justifying making something more convenient.

(B) …then new taxes…should be approved.

There’s always a wrong answer that justifies the opposite judgment. We’re not trying to support when we want to approve new taxes, we’re supporting when not to approve new taxes.

(C) …should have to pay taxes…

We’re not justifying making people pay taxes, that’s the wrong recommendation too.

(D) The best way to increase usage…

The passage isn’t really about different ways to “increase usage”, so the “best way” to do that is pretty clearly irrelevant

(E) …should be approved only when…

So if the tax doesn’t meet this standard, it should not be approved. Alright, that’s the right recommendation. This is the only one that even gets that right, so it should already be clear this is the right answer. Of course, a more careful check shows that the rest of the wording maps perfectly to the support about “few opportunities to use public libraries.”

(E) is the correct answer.

Common pattern/s in this question: The right answer is a principle, so it absolutely had to map to the exact judgment made in the conclusion. There will be virtually no exceptions to this, so recognizing this pattern is as good as carrying extra points around in your pocket.