Washer/Dryer back: Distance to Wall

So it does vary slightly from brand to brand on a washer as long as the hose isn’t crimped you can push it back till they touch, I use right-angle hoses on my washer and it sits very tight to the wall. The dryer is tricky as a dryer hose is standard 4″ diameter so that is the largest part on the back. you can also vent out the sides on select models if that helps you.  Per a few manufactures’ spec sheets I looked at they all ask for 6″  They would like about 2″ for some extra air clearance, Here is a great thing from a magnetic vent company that lines up the vent for you in tight spaces. https://www.magvent-dryervent.com/shop/mv-180-straight-vent-path-62pgk