Select the most appropriate option to fill in the blank. They don’t know how…

English uses two paired quantifier systems to ask about an unspecified quantity in the fixed interrogative frame "how ___": "how much" combines with an uncountable (mass) noun, and "how many" or "how few" combine with a countable plural noun. The quantifier "least" (the superlative of "little," marking the smallest amount in a comparison) is different: it functions as an ordinary quantifier before a noun, typically in the fixed phrase "the least," and does not open this interrogative frame.

In the sentence "They don’t know how ____ sugar is needed for a cup of coffee," "sugar" is a mass noun — it is measured in quantity (a cup, a spoonful) rather than counted as separate units — so the blank must take the uncountable-noun member of the "how ___" pair, which is "much." The completed sentence, "They don’t know how much sugar is needed for a cup of coffee," correctly asks about an unspecified amount of an uncountable substance.

• "many" pairs with a countable plural noun in this same "how ___" frame (e.g., "how many cups"); "sugar" is not treated as separate countable units here, so this quantifier does not fit.

• "few" likewise pairs with a countable plural noun in the "how ___" frame (e.g., "how few cups"); since "sugar" is not countable in this sentence, this quantifier does not fit either.

• "least" is the superlative of "little," used to mark the smallest amount in a comparison (e.g., "the least sugar of the three recipes"); it is not used to open the interrogative phrase "how ___" at all.

Reading the completed sentence back — "They don’t know how much sugar is needed for a cup of coffee" — confirms a grammatically natural, idiomatic question about quantity; substituting "many" or "few" produces "how many/few sugar," which is ungrammatical because "sugar" is not a countable plural noun, and substituting "least" produces "how least sugar," which is not an accepted English construction at all — independently confirming "much" as the correct fill.