What if you had robbling goblin trap card activaded and your opponent put an effect monster that stop the activation of trap cards will your card will be destroyed?

Answer 1

If Robbin' Goblin was already active on the field, and your opponent Summons a monster that prevents the activation of Trap Cards, Robbin' Goblin will not be affected because it was already active; it will not be destroyed.

If a card on the field prevents the activation AND negates the effects of Trap Cards (such as Jinzo), Robbin' Goblinwill remain on the field; however, its effect will also be negated.