Concept: The question tests on the application of counting
Along with the 2 hosts we have 12 guests. So there are 14 people.
Now if the master sits first, there is only 1 way that he can choose a seating arrangement as all seating arrangements are the same for him.
Similarly, once he is seated, there is only way the lady can sit, which is opposite to him.
Let us now take the 2 people sitting together. There will be 6 chairs on either side of the master and his wife. Let us say these are a,b,c,d,e and f on 1 side. Then the possible ways on one side is ab, bc, cd, de and ef which is 5 ways.
Similarly on the other side we will have 5 ways. Total ways is 10.
these 2 people can interchange (XY and YX) in 2! = 2 ways.
Total number of ways to seat these 2 people = 10 * 2 = 20 ways.
The remaining 10 guest can sit in 10! ways.
The total number of ways = 20 * 10!