assume you have 1 mole (or any other number, it doesn't matter). Mass = 206.98 g/mole. This is straight from the molar mass so that's why I like to use 1 mole
From the chemical formula, 1 mole of Ca(ClO3)2 contains 6 moles of oxygen atoms.
Mass of 6 moles of O atoms = 6 moles * 16 g/mole = 96 g
mass % oxygen = 96 g / 206.98 g * 100 = 46.4%.
You could also do it on a mole percent. 1 mole of Ca(ClO3)2 contains 9 moles of atoms.
6 moles of these are oxygen atoms so the mole % = 6 moles / 9 moles * 100 = 66.7 mole %
If you mean percent by weight or percent by composition? Ca(ClO3)2 is 67% O by composition (number of atoms) and, as calculated by Ricki, 46% by weight.