Step 1: Understand the meaning of modals.
Modals (or modal verbs) are auxiliary verbs that express necessity, possibility, permission, obligation, etc. We need to choose the modal that best conveys the required sense in the sentence.
Step 2: Analyze the context of the sentence.
The sentence describes the relationship between soldiers and the orders of their officers. In a military context, obeying orders is not optional; it is a strict requirement and a duty. This implies a strong sense of obligation or compulsion.
Step 3: Evaluate each option's meaning.
(1) need: "Need" implies a requirement or necessity, but it can sometimes be softer than 'must'. For example, "You need to finish your homework."
(2) might: "Might" expresses possibility or a weak likelihood. For example, "It might rain tomorrow." This doesn't fit the context of military orders.
(3) could: "Could" expresses possibility or ability, often in the past, or a polite suggestion. For example, "He could speak French." or "You could try calling him." This doesn't fit the context of a strict obligation.
(4) must: "Must" expresses strong obligation, necessity, or certainty. In the context of military discipline, "must" conveys the absolute requirement for soldiers to obey orders.
Step 4: Choose the most suitable modal.
Given the context of soldiers and orders, the strongest sense of obligation is required. "Must" perfectly conveys this.
$$(4) must$$