The cost of a DVD is $18.75. Added to this cost is 12% before tax fee. 5% GST, 7% PST. What is the total cost?

I suppose the 12% is the copyright fee or an environmental surcharge. Anyway, it is some kind of a surtax.

The sales taxes depend on the province in which the transaction was made.

If the transaction was made in all provinces except Quebec, both GST and PST are calculated on the purchase price (including the surtax). The total PST+GST is then 12%.
Total cost = ($18.75*1.12)*(1+0.05+0.07)
=23.52

If the transaction was made in Quebec, the PST is included in the calculation of GST.
total cost = ($18.75*1.12)*(1.05)*(1.07)
= 23.59

Double-check with your teacher the taxation rules of your province.