How could I sketch a graph of y=2x^3-3x^2?

To sketch a graph of an equation, there are several key features to consider. Firstly, we can consider where the graph crosses the x- and y-axes. When x=0, y=0, so the graph goes through the origin. If y=0, x=0 is possible, but as y=x^2(2x-3), we could also have x=3/2.
This tells us where the graph crosses the axes, so now we can ask where its stationary points are. We can find that the derivative of y is 6x^2-6x, and this is equal to zero when x=0 or x=1. To find out how the function behaves in general, think about what would happen if x is very large: x^3 will get much bigger than x^2, as it has an extra factor of x, and so for very large x, y is large and positive. This gives us enough information to find the shape of the graph.
We have found two turning points, and a cubic cannot have more than two turning points, and so we can tell from this which direction the graph will go between the turning points, and then sketch the graph.