Step 1: Picture what actually happens during extrusion.
In extrusion, a billet is squeezed hard so that it flows through a shaped die opening, and the resulting long section keeps its new cross section permanently after the die pressure is removed.
Step 2: Test each property against this requirement.
Elasticity would work against the process, because an elastic material would simply spring back to its original shape once the load is gone, which is the opposite of what extrusion needs. Ductility describes stretching under tension, such as wire drawing, and is really just one particular way plastic flow shows up, so it is too narrow a term for the general squeezing and flowing seen in extrusion. Brittleness is clearly undesirable, since a brittle billet would crack apart under the huge compressive and shear stresses rather than flow.
Step 3: Land on the property that covers the whole picture.
What extrusion truly demands is the capacity for large scale permanent flow without fracture under sustained load, and that general capability is called plasticity, it is the umbrella property that makes forming processes like extrusion, forging and rolling all possible.
\[ \boxed{\text{Plasticity}} \]