An online store lets customers have their name printed on any item they buy. the total cost c in dollars is the price of the item p in dollars plus $3.99 for the name.

So the total cost depends on the price of the item(s) (c depends on p)
The independent variable is p, the price of the item, because it is not going to depend on anything else.
The dependent variable is c, because the total cost depends on how many items there are, whether your name is marked on it, etc.
The equation would be :
c = p + $3.99

I hope this was helpful!