You are completely correct. During the Pay Cost step, you only pay 8 mana. Then during the Resolve Spell step, you resolve the effects in the order they appear on the card. So you first gain 2 mana, and then you destroy the equipment. When you go to destroy the equipment (after having gained the two mana) you must pay 2 mana due to the Rune in order to succeed at the destruction.
So, yeah, you've got it 100% right.