After a hero is assigned any amount of damage, exhaust Dori to place that damage on Dori instead.

If a hero is assigned 4 points of damage does Dori have to take it all? (Four points is any amount.)

Or do they mean that Dori can take any amount of it? Poorly phrased if so.

If a hero would take four damage from a single source (i.e., one enemy attack, one treachery effect, etc.), Dori would have to take all of "that damage."