Persons are not guilty of an offense, other than one punishable with death, that they perform under the _____ of threat or menace of imminent death or great bodily harm, upon themselves, spouse, or child, if they do not perform that conduct.

The correct answer, "compulsion," refers to the legal concept wherein a person feels forced to act in a certain way due to the imminent threat of death or significant bodily harm directed at themselves, their spouse, or their child. In legal terms, this can serve as a defense against charges for offenses committed under such duress. The idea is that the immediate threat creates a scenario where the individual feels they have no reasonable choice but to engage in the prohibited conduct to protect themselves or their loved ones.

Other terms like "apprehension" or "influence" do not accurately convey the legal principle at play here. "Apprehension" implies a sense of fear or anxiety, but not necessarily an immediate compulsion to act. "Influence" suggests a persuasive effect but does not embody the urgent necessity imposed by a threat. Thus, "compulsion" is the most appropriate choice, as it directly aligns with the legal understanding of actions taken under duress.