Since a cup holds 8 ounces, 2/3 of a cup is 5 1/3 ounces. Most measuring tools are not accurate to 1/3 of an ounce, so you may find it easier to use a different way to measure.
Using common household measuring tools, 2/3 of a cup is also equal to 10 tablespoons plus 2 teaspoons. If you have a jigger that holds 1.5 ounces, use just under four measures.
If a liquid measuring cup has measurements in metric, you can use millilitres instead. Since one cup is about 236 millilitres, two-thirds of a cup is about 157 millilitres.