I think you're almost there. Just a bit of putting the various pieces together. You've correctly identified that because the graph passes through the point (2, 0) there will be a root (or "zero") at x=2. Now you think the information that the cubic function is tangent to the x-axis at the origin tells you there's another root at x = 0. Well, perhaps looking up what it means for a graph to be tangent to the x-axis will help you. "If a graph is tangent to the x-axis, the graph touches but does not cross the x-axis at some point on the graph." Based on that, was your initial assessment correct? We also know that if the graph is tangent to the x-axis at some point (in this case the origin, x = 0) the slope is 0 at that point. What does that tell you? (Hint: You posted this in the "calculus" sub-forum; what concept have you learned that models the slope of a function?)
Finally, what information have you gained from the fact that the graph passes through the point (1, 3)? Here, you'll want to consider Subhotosh Khan's hint. What happens to the generic cubic equation Ax3 + Bx2 + Cx + D, when x = 1? What does it mean that the y-coordinate of that point is 3?
