Approach #1: Test values
The quickest approach here is to find values of X and Y that satisfy the given information, and then test those values.

For example, it could be the case that X = 32 and Y = 23, in which case X - Y = 32 - 23 = 9
Among the given answer choices, 9 is the only one that is a factor of 9.
Answer: D

Alternatively, we could have chosen X = 53 and Y = 35, in which case X - Y = 53 - 35 = 18
Among the given answer choices, 6 and 9 are both factors of 18, which means we'd have to test another pair of values in order to eliminate one of those two remaining answer choices.

Approach #2: Algebra
Let X = jk, where j is the tens digit of X, and k is the units digit of X
This means Y = kj, where k is the tens digit of Y, and j is the units digit of Y

Important: Keep in mind that a two digit number such as 27 is really just a recipe for the VALUE of that number.
For example, the VALUE of 27 = 2(10) + 7(1)

Similarly, the VALUE of X (aka jk) = 10j + k
And the VALUE of Y (aka kj) = 10k + j

This means X - Y = (10j + k) - (10k + j)
= 9j - 9k
= 9(j - k)

Since X - Y = 9(j - k), we can see that 9 must be a factor of X - Y

Answer: D