Let   i = my age now,
      b = my brother's age now,
      s = my sister's age now,
      f = my father's age now, and
      m = my mother's age now.

Now I will algebreze the condition, by writing the equation/expression for each statement of the problem.

1. "My brother is 3 years elder to me."                      ---> b = i + 3      (1)
2. "My father was 28 years of age when my sister was born"   ---> f = s + 28     (2)
3. "my mother was 26 years of age when I was born"           ---> m = i + 26     (3)
4. "my sister was 4 years of age when my brother was born"   ---> s = b + 4.     (4)

We have 5 unknowns and only 4 equations. But still keep the positive attitude.

What do they want? - They want from us to find  f-b.   OK.

f - b = (s+28) - (s-4).   (5)   <--- I replaced f by (s+28) based on (2), and replaced b by (s-4) based on (4).

So, I can continue (5) in this way:

f - b = s + 28 - s + 4 = 32.

It is just the answer to the problem's question:


   "what was the age of my father when my brother was born?" - The father's age was 32 years at that time.


The problem is solved.


Probably, there is a shorter way to solve the problem.
But developing this solution, you learned so many things, that our efforts are justified.


It seems to me that a young reader may have a question: 
   how it could happen that we were able to solve the system of 4 equations in 5 unknowns?

The answer is: we didn't solve the system.
We only found the value of some expression ("f - b" in this case) of the variables, based on given equations.
But we didn't solve the entire system.

Also, you may see that we used only some part of the given data, and didn't use all of them. 
It is also the trick of the authors of the problem: They included a non-necessary information to miss the readers. 

But, happily, we were not missed.

In whole, this is brilliant/outstanding problem.
Thanks to its authors and to the sender for posting it.