Up : Down :: Factor : Multiple

Explanation:
To solve this analogy, we need to understand the relationship between the given words.

Up and Down:
The words "Up" and "Down" are antonyms, meaning they have opposite meanings. When we go up, we are moving in an upward direction, and when we go down, we are moving in a downward direction. Therefore, "Up" and "Down" are antonyms.

Factor and Multiple:
The words "Factor" and "Multiple" are related to multiplication and division.

Factors: Factors are the numbers that can divide a given number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Multiples: Multiples are the numbers that can be obtained by multiplying a given number by any whole number. For example, the multiples of 4 are 4, 8, 12, 16, 20, and so on.

Relation between Factor and Multiple:
The relationship between factors and multiples is that the factors of a number are the numbers that divide it evenly, while the multiples of a number are obtained by multiplying it by other numbers.

Application of the Relationship:
Now, let's apply this relationship to the given analogy.

Up : Down :: Factor : ?

Since "Up" and "Down" are antonyms, we need to find a word that is related to "Factor" in a similar way.

Answer:
The word that is related to "Factor" in a similar way as "Up" is related to "Down" is "Multiple".

Therefore, the correct answer is option A) Multiple.

12+12