For the standard deviation of the set to be greatest, there must be a considerably big difference between one or few data in the set and the arithmetic mean of the set, that is one has to look for the maximum possible absolute value of (x - A), where x is a random data from the set and A is mean of the set; which is 12 in our case. In this case, for the mode to be x, there must be at least 3 appearances of x as there are already two appearances of 16 there, which is not openly told the mode, which might well have been the mode if x were 16, in fact x can take any value given in set EXCEPT y, to be the mode of the set, but! We will take only that as x which maximizes the absolute value of (x - 12), of the given values, only 16 works, CANNOT take 18, as this won't make x the mode ahead of 16. Take D

Thanks sanju09!