Words that count days use an exceptional reading. Even though this is a jukugo word, it uses kun'yomi readings for both the kanji. Think about this word this way:
Every eighth day you have to buy yogurt to fuel your car (ようか). Your car runs on yogurt, but it needs to be refilled every eight days to keep running. It's really inconvenient because it's just ONE day more than a week. And a week just feels better. Oh well.
My summer break is eight days long.
Could you please give me some water? I haven't eaten anything for eight days.
I’m going to get hemorrhoid surgery on the eighth of next month.