I can't imagine that it's more than $6,000 per month. Cloudflare's enterprise service is a flat $5,000 per month regardless of utilized bandwidth, and can be negotiated downward. The dedicated server hosting 4chan's code and UGC cannot cost much more than $1,000 per month.

I run a site with a slightly better alexa ranking than 4chan. I've read past 4chan blog entries so I know that the traffic demands are similar, and my own expenses average around $6,000 per month.