Option 1: Boiling - Boiling water is effective in removing temporary hardness but not permanent hardness. Permanent hardness is caused by the presence of insoluble compounds such as calcium sulfate and magnesium sulfate, which cannot be removed by boiling.

Option 2: Ion-exchange - This method involves passing the hard water through a special resin that contains exchangeable ions. The resin exchanges the calcium and magnesium ions in the water with sodium or potassium ions, effectively removing the hardness. This process is commonly used in water softeners.

Option 3: Lime treatment - Lime treatment is effective in removing temporary hardness but not permanent hardness. It involves adding slaked lime (calcium hydroxide) to the water, which reacts with the calcium and magnesium ions to form insoluble precipitates that can be removed.

Option 4: Bubbling sulfur dioxide gas - This method is not effective in removing permanent hardness. Sulfur dioxide gas may react with the dissolved oxygen in water, but it does not have a direct effect on the calcium and magnesium ions that cause permanent hardness.

In conclusion, the correct method for removing permanent hardness of water is ion-exchange (option 2).