Great question, @elmullet! 3456px longest edge is close enough.
We get the 3600px number by multiplying the number of inches we want to print (12 inches) by the density of pixels per inch that’s best for viewing a printed image (300 pixels per inch). However, it could be that the designer may not actually end up using the photo to cover the entire background (thus being printed at smaller than 12 inches), and even if he does, the print quality is still acceptable at a lower ppi (so, like 250 ppi can still look pretty good). Furthermore, if needed, some images (especially if taken in RAW) can be up-sampled in post processing fairly well, which brings me to the conclusion that 3456px longest edge would be sufficient.