Okay so first you have to count up the number of elements on each side of the equation. Your objective is to have the same number of each element on both sides.
Left Side: Zn - 1 S - 1 O - 1
Right Side: Zn - 1 S - 1 O - 2
Since there are two oxygens on the right side, you have to add a coefficient of 2 to the oxygen on the left side. The coefficient tells us that that element or molecule is being multiplied by the value of coefficient. Since we're adding a coefficient of 2 to the oxygen on the left side, there are now 2 oxygens on that side. Because that is the same amount of oxygen as on the right, the equation is now balanced.
Your final equation should look like this: ZnS + 2O --> ZnO + SO
