You can put this solution on YOUR website! Because f(x)=2^x, the graph of g(x) = -2^x will be INVERTED (that is, upside down!), and because of the -2 at the end, the values of g(x) will all be 2 units lower on the graph (that is, a vertical shift DOWN 2 units!).
The graph below illustrates f(x), then f(x) inverted, then g(x), which is actually f(x) inverted and shifted down 2 units: