f(3x – 2) = 0
The previous reply assumed that there was a floating open "dot" or circle between the "f" and the "g", so that this is function composition. If that assumption was mistaken, then this would appear to be operations on functions. In which case, multiply the expressions for f and g, set equal to zero, and solve the resulting equation. Since the expression for f factors easily, it's simple to find all three factors, which solve (as simple linear equations) for the three solution values.
What class are you taking? This question probably belongs in that topic's forum. As for lesson instruction, we can't really provide that here; that's why there's a textbook and a course instructor. But you can try self-study online, if you'd like. How much of this do you not understand? Functions? Polynomials? Solving algebraic equations? Factoring quadratics and differences of squares? Or something else?
If what you meant to write was f(g(x)), then this problem involves composition of functions. There are probably a number of related tutorials on line. Here is the URL for one: http://www.youtube.com/watch?v=S4AEZElTPDo