Balancing equations in chemistry demonstrates the law of conservation of mass, by counting the number of atoms on both sides of the yields sign.  It is important to make sure you write the original equation down correctly before you start trying to balance the equation.  If you look on the left side of the equation, you have the formula for magnesium chlorate correctly written Mg(ClO3)2.  The magnesium ion will have a charge of +2 upon dissociation, and the chlorate ion will have a charge of -1 upon dissociation.  It is important to remember magnesiums +2 when you pair the magnesium and the chlorine atom to form magnesium chloride on the products side of the yields sign.  It should be written MgCl2, not MgCl.  It will take two chlorine atoms to pair with the +2 charge of the magnesium ion.  Once you make that simple correction, balancing the equation falls into place:

Mg(ClO3)2 ---> MgCl2  +  3O2