Il n’a que deux frères - He only has two brothers. Is this correct? or it should be - He has only two brothers?

Both versions of the English translation are possible, because the difference between them is, at most, ephemeral. ;)

In French you could only reasonably say, "Il n'a que deux frères." Because "il ne qu'a deux frères." sounds impossible to my ears. 

Thanks Chris for your response.

He only has two brothers can also mean - He and only he has two brothers out of a group of people. Sounds like an overkill but since this translation belongs to a quiz, I was wondering that after all the learning on where to put 'only', why would the answer be in a different way.

You'd teally need tone of voice, too, to help you nail down the meaning exactly.