If you double the volume of a sample of gas and then doubled the volume again without changing its pressure, how would this absolute temperature of the gas be affected

Increasing Volume while maintaining constant pressure requires a proportional increase in Temperature so the gas pressure will be maintained as constant.

Consider ...

V₁ = V₁ V₂ = 4V₁

T₁ = T₁ T₂ = ?

Charles Law = > T ∝ V at constant P ... that is, increasing temperature generates a proportional increase in volume to maintain constant pressure.

Empirical Charles Law Relation is ...

V₁/T₁ = V₂/T₂ = > T₂ = T₁ (V₂/V₁) = T₁ (4V₁/V₁) = 4T₁

Increasing Volume of a gas by 4 times requires a 4 times increase in absolute temperature in order to maintain constant pressure.

absolute temperature will increase fourfold