A quadratic's discriminant can either be more than zero, less than zero, or exactly zero. When the discriminant is less than zero, there are no real solutions and the graph won't cross the x-axis. When it's exactly zero, there will be a real double root and the graph is tangent to the x-axis. When it's more than zero, there will be two real solutions and two x-intercepts.
Our graph has two intercepts, so it needs a positive discriminant more than zero. Choice A's is negative - no.
Choice B's is zero - no.
Choice C's is positive -yes.
Thus, "C" is the possible discriminant for the given graph.