Explanation:

Any number between 100 and 600 must be of three digits only.
2,  3, or  4
Since the number must be greater than 100
So hundreds place can be filled up by any one of the three digits 2, 3, and 4 in 3 ways.
Remaining two places can be filled up by the remaining five digits 5P2 ways.
Required number = 3 × 5P2 = 3 × 5! /3!
                                                   
= 60