In this expansion we know that there are 13 terms which mirror each other starting with x and ending with 1. We know that the 6th power is in the exact middle of the expansion and thus will be the largest coefficent. Here is the expanded version
x^12+ 12x^11+ 66x^10+ 220x^9+ 495x^8+ 792x^7+ 924x^6+ 792x^5+ 495x^4+ 220x^3+ 66x^2+ 12x+ 1
As you can see, the 6th power term is the greatest coefficent and the other terms mirror one another moving away in both directions.