If 82.3 l of an ideal gas is cooled from 46 degrees calius to - 166 what will the volume of the gas become

Temperature is directly related to volume. Note that temperature used is Kelvin, so you need to convert both of them into Kelvin

With that information, you can derive this equation:

T1/T2=V1/V2

V2 = V1*T2 / T1

V2 = 82.3 * (-166+273.15) / (46+273.15)

V2 = 82.3 * 107.15 / 319.15

V2 = 27.63L