Heres the situation my opponent has three s/t face down i summon Mobius i choose two of the set cards then my opponent activates trap hole so my question is at what time must my opponent activate trap hole when mobius is summon or after his effect activates?

Traps activated in response to the summon of Mobius are activated after his effect triggers.

Mobius's effect and m/t targeting happens as soon as he is Tribute Summoned successfully.

This is the same time that Trap Hole, Bottomless Trap Hole, Torrential Tribute, etc are to activate.

So your opponent would Tribute Summon Mobius and immediately decide how many cards to target: 0, 1 or 2. In this case, he selected 2.

Afterwards, when priority is passed to you to activate cards, you can chain with Mobius's activation with Trap Hole, Bottomless Trap Hole, Torrential Tribute, etc, etc, even if it is one of the targeted cards (the cards are not destroyed until Mobius resolves in the chain).

Then the chain resolves backwards with, in this case, Trap Hole destroying Mobius and then Mobius destroying Trap Hole and the other targeted m/t, assuming that it is not also chained.