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To find out how much of the pizza Henry ate for dinner, we first need to calculate how much pizza was left after lunch.
If Henry ate 3/8 of the pizza for lunch, then 1 - 3/8 = 5/8 of the pizza was left after lunch.
Next, if Henry ate 2/3 of what was left from lunch for dinner, then he ate 2/3 * 5/8 = 10/24 = 5/12 of the pizza for dinner.
Therefore, Henry ate 5/12 of the pizza for dinner.