I just looked through my notes, and it appears that my last 6-8 encounter day was... last game, with most of the day happening the game before (well, the game before for that group, anyhow- I run multiple parties).
I run a hardcore sandbox, so I don't use the encounter building design guidelines at all. With that in mind, the party included:
Buford (fighter 9)
Windsor (wizard 8)
Karn (cleric 6)
..and, for the last two encounters:
Bast (cleric 5)
The encounters were with:
2 troglodytes
1 phantom fungus (homebrew conversion of the 3e monster)
4 troglodytes
8 troglodytes and a unique two-headed troglodyte worshiper of Demogorgon
1 ettin
1 headless (homebrewed monster, CR 5)
13 stirges
9 stirges
This is not too atypical for my game, at least when a party is dungeoneering (which is pretty common). Interestingly, the player of Karn tends to blow through all his resources (ki points, spells, whatever) very quickly no matter what character he's playing, and this holds true with Karn. This means that the later encounters are much harder on him than the earlier ones are. However, the last few games, he's actually been conserving some resources- he still had a third level slot left to cast spirit guardians against the 13 stirges.
Buford is a battlemaster, so he regains lots of tactical options on a short rest. He's not shy about spending his superiority dice, but he also doesn't use them wastefully. So a long day like this one, which I think had one or two short rests in it, serves him pretty well. Paradoxically, it also gives him more effective hit points, because he can use his second wind more due to having more short rests.