A hunter was asked how many birds he had caught and had in his bag. He replied that there were all parrots but eight, all ducks but eight, and all swans but eight. How many birds did he catch in total?

Let the total number of birds in the bag be $T$.
* "All parrots but eight" means the number of parrots is $T-8$.
* "All ducks but eight" means the number of ducks is $T-8$.
* "All swans but eight" means the number of swans is $T-8$.

Since these are the only types of birds in the bag, the sum of these birds must equal the total number of birds $T$:

$$T=(T-8)+(T-8)+(T-8)$$

$$T=3T-24$$

$$2T=24⟹T=12$$

Thus, the hunter caught 12 birds in total.