This sentence can be checked by applying two fixed rules for "neither" one after another, rather than reading each option separately.
The first rule is about the partner word. "Neither" always pairs with "nor" to form one linking unit, "neither...nor." Words like "and" or "but" cannot stand in for "nor" in this pair, since they signal addition or contrast, not an either-or choice between two things.
The second rule is about the verb. When "neither...nor" links two singular subjects, here "this" and "that machine," the verb that follows also stays singular. So the correct verb is "is working," not "are working."
Applying both rules together: the sentence needs "neither" paired with "nor," followed by the singular verb "is." Any option missing either piece fails the check.
So, the correct answer is Neither this nor that machine is working.
Reading each option aloud and noticing which word feels wrong the moment it is spoken is a quick way to settle this one.
Trusting where the ear stumbles and then checking why confirms the same choice every time.
So, the correct answer is Neither this nor that machine is working.