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 be $T$, the number of parrots be $P$, ducks be $D$, and swans be $S$.
Therefore, $T=P+D+S$.

According to the given problem:

1. "all parrots but eight" means: $T-P=8⟹D+S=8$
2. "all ducks but eight" means: $T-D=8⟹P+S=8$
3. "all swans but eight" means: $T-S=8⟹P+D=8$

Adding all three equations together:

$$(D+S)+(P+S)+(P+D)=8+8+8$$

$$2P+2D+2S=24$$

$$2(P+D+S)=24$$

Since $P+D+S=T$:

$$2T=24⟹T=12$$

So, he caught a total of 12 birds (4 parrots, 4 ducks, and 4 swans).