How to move forward in balancing this equation?
The reason you cannot balance the reaction is because you did not consider everything that happens. In the Prilezhaev epoxidation, mCPBA is a stoichiometric reactant but only one single atom of mCPBA is transferred to the product. Therefore, these compounds are often written on the reaction arrow rather than as reactants and products:

$$\ce{C14H12 -&gt;[C7H15ClO3] C14H12O}\tag{1}$$

However, that still does not tell you what exactly happened. If you take a close look at the mechanism, you will see that mCPBA remains essentially unchanged except that it loses its peroxy function; the second product is mCBA or meta-chlorobenzoic acid. Thus, a full reaction equation would be:

$$\ce{C14H12 + C7H15ClO3 -&gt; C14H12O + C7H15ClO2}\tag{2}$$

Notice how this balances automatically.