Let us calculate the minimum number of people who get accommodations in hotels they prefer.
30% will be given hotel XYZ and 45% prefer hotel ABC.
Suppose all 30% who are given XYZ come from 45% of who prefer ABC.
So (45 - 30)% or 15% get ABC which they prefer.
70% will be given ABC.
So (70 - 15)% or 55% is available in ABC.
It has already been given that 55% prefer XYZ. Let all of them be fitted into ABC so as to minimize the number of people who get the hotels they prefer.
Or we get that only 15% get the hotels they prefer.
So 85% do not get the preferred hotels.
This amounts to 85% of 60 = 51.
So the maximum number of people who do not get accommodations they prefer is 51.

naremnaresh wrote:30% of 60 = 18 has to stay in ABC
70% of 60 = 42 has to stay in XYZ

55% of 60 = 33 prefer to stay in xyz
45% of 60 = 27 prefer to stay in ABC

consider that outof 33 (who prefer to stay in xyz) 18 are accomodated in ABC
count = 18(who do not get the accommodation they prefer)
the remaining 33-18 = 15 and 27 are accomodated in xyz. out of these 27 donot get there preferred choice.
so count = 18 + 27 = 45(who do not get accommodations they prefer)

45 is the correct answer.

The first part of your solution is not correct.
It should be:
30% of 60 = 18 has to stay in XYZ.
70% of 60 = 42 has to stay in ABC.
What you have done is the reverse.