One day on the counter at room temperature is approximately equivalent to a week in the refrigerator. When I used eggs at a rapid rate, baking every day, I always kept them on the counter, since they would not have to be brought to room temperature to beat easily to the ribbon or whatever.
They should be good in the refrigerator for several weeks past their sell by date, or on the counter for several days.
6 hours is fine.
(All of the above is assuming they are in their shells, uncracked....)
Out of the shell, eggs are highly perishable--what the health codes call a "potentially hazardous" food. Don't hold them for any length of time at room temperature. I would say no more than 30 minutes to an hour, less if you can.
Lots of egg facts, but they do insist that the eggs are refrigerated.