Acc to the ques 11 YEARS earlier the average age of a family of 4 members was 28 years, that means:

Total age of 4 members was = 28 x 4 = 112

So, after 11 yrs the total age must be = 112 + (4 x 11) = 112 + 44 = 156.

Acc to ques, now 2 children are added to the family.

Thus total age = 156 + age of 2 children.

avg age of 6 members = (156 + age of 2 children)/6 = 28 [as it is given in the question the average age of the same family with six members is yet the same]

or, age of 2 children = (28 x 6) - 156 = (168 - 156) = 12.

Now, again it is said that the age of the first child at the time of the birth of the younger child was same as there were total family members.

That means age of elder child during birth of younger child was equal to no of family members = 6.

Now the climax:

since age of 2 children = 12; it doesn't means the younger will be 12 - 6 = 6.[because, it doesn't MAKES SENSE that both will be 6yrs old]

but, you have to divide that time by 2. i.e.

The elder is of 6+3 = 9 yrs. and younger = 3yrs.