Step 1: Define the fluid behaviors.
A. Shear-thinning (Pseudoplastic): Viscosity decreases as shear rate increases. Shaking or stirring makes it flow more easily. Tomato ketchup is a classic example. So, A-I.
B. Newtonian: Viscosity is constant regardless of shear rate. Milk (and water) behaves approximately as a Newtonian fluid. So, B-II.
C. Shear-thickening (Dilatant): Viscosity increases as shear rate increases. It becomes thicker when stirred or hit. A concentrated corn starch solution is the prime example. So, C-IV.
D. Bingham plastic: Behaves as a rigid solid at low stress but flows like a viscous fluid at high stress. It has a "yield stress". Whipped cream, toothpaste, and mayonnaise are examples. So, D-III.
The correct set of matches is A-I, B-II, C-IV, D-III.