I'm not myself concerned all that much about conserving water, but I am a normal person, so I don't wash my dishes under running water. I fill the sink up with water, stick in some washing-up liquid as it fills, then once it's mostly full (12-15L of water?) I use that. Total use per wash is then 12-15L. Maybe a bit more if I give something a rinse. (Very much optional in my view for most items - but some things do need it.)
You can wash a lot of stuff in that much water! So that's why I am a bit surprised at people using 120L to wash twelve places'-worth. That's eight times the amount I'd use for washing 3-4 people's-worth of stuff and all the items used to prepare the food in the first place.
(I think my dishwasher uses 17L per wash so I don't worry too much about using that instead. I am quite lazy.)