If i chose with goblin king invincible and impervious at the beginning of the turn, and my opponent attack my goblin king, when I can chose which defense I use:
-before the attack ? Or
-after I undesterstand to be hitted?

After the successful attack roll, I believe.

Page 15 of the rulebook covers that questions and the flow of an attack

So goblin king chooses the difence after attack roll.
Thank you

True, but not so fast! It actually comes a little later than this. You can wait until the damage is assigned and effects that modify damage dealt occur. So when splitting damage, the attacker doesn't get the benefit of knowing which reducer you will choose.