I found a really nice shop selling small kitchen appliances, like coffee makers, so do you want to go there with me week after next?
You know how 来週 is next week? Well, if you do next week again, you have the week after next.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.