Is there an easy way to cool water to temperatures around -20 or -30 degree celsius that is economically and technologically feasible for a high school student. Can it be done using typical household equipments? Thanks :)
Some domestic, commercially marketed deep freezers are able to reach that range of temperature. Here is one for example that advertises -20deg F, so almost -30 deg C.
It really depends also on the amount of mass you want to lower the temperature to. Whatever device to be considered must provide outward heat flow to compete with whatever heat influx the mass would be exposed to from the environment. Here's an idea. For a small amount of mass you can use endothermic chemical reactions which absorb heat. For example barium hydroxide octahydrate and ammonium thiocyanate. If you mix these two chemicals in the right stoichiometric ratio you can reach cold enough temperatures to freeze water in seconds. See the Demo Here.
But careful, barium compounds are toxic. Also not your everyday household item.
"typical" household freezers don't do minus 20. A premium dedicated freezer (no fridge part) might, but I don't think you want to buy one just for this.
For a low-budget solution, get a styrofoam cooler, put your regular-temperature ice in it, and then add 2x mass dry ice. You will eventually get colder ice.
Do cut a small drain hole in the bottom of the box, you will get liquid water at the beginning of the process.
Don't tape or latch the lid shut. The evolving CO2 gas needs to escape.
Don't do this in an enclosed room or basement either.
Don't quite know what you mean by "water at -20 degrees", as I would expect ice at these temperatures. But anyways you can reach such temperatures with a cooling bath