You must have seen the graph of y=x^3. Plot that first.
Step 1. Graph of y=2f(x) has the same shape as the graph of y=f(x), but compressed horizontally by a factor of 2.
To sketch y=2x^3, look at the graph of y=x^3, and compress it horizontally by a factor of 2, i.e. new y values are twice as big as they were in y=x^3 for the same x.
Step 2. Graph of y=g(x-2) has the same shape as the graph of y=g(x), but shifted 2 units to the right.
To sketch y=2(x-2)^3, shift your previous graph 2 units to the right.
Step 3. Graph of y=h(x)-7 has the same shape as the graph of y=h(x), but shifted vertically 7 units down.
To sketch y=2(x-2)^3 - 7, shift your previous graph 7 units down.
