The key concept here is that, for every arrangement in which 'A' comes before 'D', there is an arrangement in which 'D' comes before 'A'
In other words, in HALF of the arrangements, 'A' comes before 'D' and in HALF of the arrangements, 'D' comes before 'A'

To better understand what I mean, let's look at a smaller example:
Let's list all 6 arrangements of the letters in the word BAD:
ABD
ADB
BAD
BDA
DAB
DBA
In the first three arrangements, 'A' comes before 'D'
In the last three arrangements, 'D' comes before 'A'


The same applies to the five letters in the word AUDIT
We can arrange the five letters in 5! ways (= 120 ways)
In HALF of those 120 arrangements, 'A' comes before 'D'

120/2 = 60

Answer: B

Cheers,
Brent