Deionised water is a type of water that has had most or all of its mineral ions (such as calcium, magnesium, and sodium) removed. The correct method for producing deionised water is the ion-exchange resin process, which is represented by option 2.

Option 1, the calgon process, is not a method for producing deionised water. Calgon is a brand of water softener, which is used to remove hardness-causing minerals from water. While it may reduce certain ions, it does not completely deionise the water.

Option 3, the dark`s process, is also not the correct method for producing deionised water. The Dark`s process is used for the production of industrial-grade sodium hydroxide and chlorine gas through the electrolysis of saltwater.

Option 4, the permulti process, is not a recognized method for producing deionised water. It seems to be a made-up term that does not have any relevance to water purification.

In summary, option 2 - the ion-exchange resin process - is the correct method for producing deionised water, while the other options do not pertain to the deionisation process.