Sorry to say but certainly no. Your power can deliver max 12*2 (Volt times Ampere) Watt. Your peltier cooler require 12*6 Watt. And it is no possibility that this can come from your current power supply
Yup that's what I do. I use the 5V supply for my 12V peltier, to run it well below capacity. It's more efficient at lower current, and my PSU has more 5V amperage available anyway.