Let’s solve this question via the most basic of counting techniques, the Fundamental Counting Principle (FCP):

As always, we’ll begin the most restrictive stage(s):
Stage 1: We can seat person B in 6 ways (seat B in chair 1, 2, 3, 4, 5 or 6).
Stage 2: At this point, we can seat person C in 1 way (directly across from person B).
Stage 3: We can seat person A in 4 ways (any remaining seat that isn’t yet occupied)
Stage 4: We can seat person D in 3 ways (any remaining seat that isn’t yet occupied)
Stage 5: We can seat person E in 2 ways (any remaining seat that isn’t yet occupied)
Stage 6: We can seat person F in 1 way

Now apply the Fundamental Counting Principle to see that the total number of ways to seat all 6 people = (6)(1)(4)(3)(2)(1) = 144

Important: Since two seating arrangements are considered different only when the positions of the people are different relative to each other, we see that we’ve counted each unique outcome 6 times.

For example, these 6 arrangements . . .

. . . are considered 1 unique arrangement because the relative positions of the six people are the same in each case. .

So, to account for counting each arrangement 6 times, we’ll divide 144 by 6 to get 24, which means the correct answer is B.

Answer: B