(I'm assuming you mean liquid ounces here.) There are eight ounces in a cup. 2 ounces is 1/4 of that number, or 1/4 of a cup. For those who can't find their quarter cup measure, there are two tablespoons per fluid ounce, so that's four tablespoons of liquid.
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2 cups equal 16 ounces. However, if you're pregnant, for instance, this measurement changes, to 2 cups equal 12 ounces. This was made known to me by my gynecologist and a nutritionist during my pregnancy.