Which of the following is a contraindication for administering Acetaminophen?

Administering acetaminophen within four hours of a previous dose is a clear contraindication due to the potential for toxicity. Acetaminophen has a maximum recommended dosage, and exceeding this limit can lead to serious health risks, including liver damage. Administering it again too soon could push the patient beyond this threshold, especially if they had already taken acetaminophen recently.

Other factors like unaltered mental status, history of fever, or current cough do not inherently contradict the safe administration of acetaminophen. These conditions do not affect the medication's effectiveness or safety directly; thus they do not prevent its use in the same manner that a recent dose within four hours does.