Brownexed is a word commonly used in Mid-Western American subculture to refer to someone's opinion being absolutely steamrolled and proven wrong a.k.a getting figuratively shitted on.
It probably originates from the color of shit itself, with reference to the shit overtaking the opinion at hand; this draws similarity to the phrase 'whitewashed'. It is essentially a form of ownage.
Dude 1: "I think if I recycle I can make a difference in the world."
Dude 2: "You douchebag, good luck convincing all of China to do the same, not to mention the rest of the world. Think before you speak."
Dude 1: "Wow...I just got totally brownexed...this is awkward"
Dude 2: "I think I fancy you..."