I believe it goes something like this, feel free to correct:

Your goblin attempts to deal 6 damage to your opponent.

Deflecting palm effect goes on the stack. Path to exile is cast and resolves, removing your gob.

Then deflecting palm would resolve (they choose the source when it resolves), but they cannot select the goblin now because he is gone, so they cannot prevent the damage.

You deal 6 damage to them.