Step 1: Focus on the key phrase in the question, high pressure filling.
The question is really asking which casting method relies on forcing molten metal into the mould cavity using external pressure, rather than simply letting gravity or spinning do the work.
Step 2: Rule out the gravity and rotation based methods.
Slush casting pours metal in under gravity and then pours the excess liquid back out, no pressure injection involved. Centrifugal casting relies on the mould's rotation to fling metal against the walls, not on external pressure. Permanent mould casting, despite using a reusable metal mould, is normally filled by simple gravity pouring, which is why it is also called gravity die casting.
Step 3: Match the description to die casting.
Die casting is defined precisely by injecting molten metal into a reusable metal die under substantial applied pressure, which forces the metal to fill even fine intricate details quickly before it can solidify. This rapid, pressure driven filling is what gives die castings their fine grain structure and smooth surface finish, and it directly matches the high pressure description in the question.
\[ \boxed{\text{die}} \]