I would think the syncronizer unit is (supposed to be) blowing excess air OUT thru those hoses into the air box for later ignition (I may very well be wrong). They appear to be on the clean side of the air filter assembly, perhaps just venting?
Looking at the parts fisch there called "Pipes" :
http://www.partzilla.com/parts/search/Yamaha/Motorcycle/2004/FZ6+-+FZ600SS/INTAKE+1/parts.html .
Checking the shop manual, syncing etc, it doesn't address what they do short of connecting the air box to the syncing box. Randy's had his apart a bunch of times, he'll likely chime in, I'm curious as to what exactly they do..
In either case, I'd remove each hose and take a peek down both ends. The part into the air box, probably pull the air filter and blow air thru there getting rid of any loose dust. As for the other end, take a peek, look for anything un-usual, maybe some (a little) brake cleaner if carboned up/greasy and wipe it out quickly with a clean rag..
I guess who ever had the air box off last missed those two big hoses upon re-assembly
You may want to peek around a little bit for anything else un-usual or out of place.
BTW, as clean as it is (it looks BRAND NEW) and as well as it runs, I seriously don't think you'll have an issue with it pnce assembled correctly.
Marco Polo Randy!