Put rice in a large, heavy pan. Add water, dashi and 4 tsp. sugar; soak about 2 hours. Cover and bring to a boil over high heat until the water begins to spew out from the lid. Without lifting the lid, turn heat to low (on an electric range, have one of the units preheated to low and immediately transfer the pan of rice). Cook for 12 minutes on low heat; remove from heat and let stand 10 minutes, all without lifting the lid. Meanwhile, combine in a small pan, rice wine vinegar, 6 Tbls. sugar, salt and mirin; heat just until sugar is dissolved. Have ready an electric hair dryer or have someone standing by who can fan the rice mixture to cool it quickly as you add the vinegar mixture (this prevents the rice from becoming soggy). Turn the cooked rice immediately into a large bowl and carefully fold in the vinegar mixture while fanning or cooling it with the hair dryer set on “cool,” being careful to keep the rice grains whole. If you use a rice cooker, use a cup measure, and not the small one that comes with the cooker. Let the rice and water stand for two hours before covering and turning the cooker on.