The mean of a binomial distribution where there are: 

n trials with a probability p of ONE sucess in ONE trial,

is given by  m = np.  

The nearer a number of successes is to the mean of m = np, 
the more likely it is to occur.

In this case np = (25)(0.48) = 12.

Therefore the most likely number of successes is 12.
The next most likely is 10, the next is 9, and the least likely is 20.

P(20 sucesses) < P(9 sucesses) < P(10 successes) < P(12 sucesses) 

FYI, by actual calculation,

P(12 successes) = 0.15811
P(9 successes) = 0.07897
P(20 successes) = 0.00085
P( 10 sucesses) = 0.11664

The correct answer is, of course, P(12 successes).

Edwin