It depends on what unit you are trying to convert it to. Here is a tip; type the following into Google: two thirds ounces to __________ Inserting the unit you want into the blank (tablespoons or milliliters for liquid, grams or pounds for solids) and it will tell you precisely how much it would be.
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Well, if a Cup is equal to 8 oz. then what you would do is divide 8oz, by 3 (thirds), then multiply by 2 (of the 2 part of 2/3rds) to get your answer.
This isn't an even number of ounces.
Begin with 8/3 = 2.67
Then you would take 2.67 x 2 = 5.33 ounces in 2/3rds of a Cup