When a quantity of monatomic ideal gas expands at a constant pressure of 4.00*104pa, the volume of the gas increases from 2.00*10-3m3 to 8.00*10-3m3?

Yes that is correct. We know this because 4.00 x 10 4 Pa is constant. If you have 2.00*10-3m3 then you do the following: (2.00*10^-3) (4.00*10^ 4) = 8.00*10^-3. That is how you get your answer

This can be verified if we know the values of the initial (T1) and final (T2) temperatures. We use the ideal gas equation for this: PV=RT.

P1V1=RT1

(40000 Pa) * (0.002 m^3) = (8.314 m3Pa/molK) (T1)

T1 = 9.62 K

P2V2=RT2

(40000 Pa) * (0.008 m^3) = (8.314 m3Pa/molK) (T2)

T2 = 33.5 K

Thus, this is true if the monoatomic ideal gas is heated from 9.62 K to 33.5 K at constant pressure.