Step 1: Understand the two types of hardness.
Temporary hardness is caused by bicarbonates of calcium and magnesium. Permanent hardness is caused by chlorides and sulphates of calcium and magnesium, these salts do not break down on heating.
Step 2: Check what boiling does.
Boiling only decomposes the bicarbonates present in temporary hardness, turning them into insoluble carbonates that settle out. Chlorides and sulphates of calcium and magnesium remain fully dissolved even after prolonged boiling, because they are thermally stable in water.
So boiling cannot remove permanent hardness, option D is correct.
Why the others are wrong: Adding sodium carbonate (option A) precipitates calcium and magnesium as insoluble carbonates, this works on permanent hardness too, so it is not the answer. Distillation (option B) converts water to vapour and leaves all dissolved salts behind, so it removes both types of hardness completely. Adding caustic soda (option C) converts calcium and magnesium salts into insoluble hydroxides and carbonates, this also removes permanent hardness. Only boiling fails to work on permanent hardness.