A bird lover was asked how many birds he had in the basket. He replied that there were all parrots but six, all pigeons but six, and all koel but six. How many birds he had in the basket in all ?

There were all parrots but six means that six birds were not parrots but only pigeons and koels.

Similarly, number of parrots + number of koels = 6 and number of parrots + number of pigeons = 6.

This is possible when there are 3 parrots, 3 pigeons and 3 koels i.e. 9 birds in all.