Solution; 

Let the ages of four children born at an interval of 4 years each be x , (x + 4) , (x + 8) and (x + 12).

Here the youngest is the child with the age of 'x'.

Given: Sum of the ages of four children = 60

x + (x + 4) + (x + 8) + (x + 12) = 60

 x + x + 4 + x + 8 + x + 12 = 60

4 x + 24 = 60

4 x = 60 - 24

4 x = 36

x = 36/4

x = 9

So the age of the youngest child is 9 years.

The correct option is 2). 9 years.