With no change in the amount of material in the flask, the volume of the container in question is increased to 5.000 times the original. Assuming constant temperature, calculate the (new) total pressure, at equilibrium
The total pressure in equilibrium equals the sum of the equilibrium partial pressures: P = p(N₂O₄) + p(NO₂) = p₀ - x + 2∙x = p₀ + x = 4 atm + 0.641 atm = 4.641 atm
Because p(x)∙V = constant for an ideal gas under isothermal conditions, quadrupling volume quarters the partial pressures. To solve the part you could adjust the equilibrium partial pressures from previous part and then set up a new ICE table and find the new x. I would solve in different way. For the final equilibrium it makes no difference if you let equilibrium establish, change the volume and let reestablish equilibrium volume or if change initial volume thus initial pressure and let establish equilibrium.
So all you need to repeat calculation above with an initial pressure of: p₀ = 4atm / 4 = 1atm => x = (Kp/8)∙[√( 1 + 16∙p₀/Kp) - 1] = (0.490/8)∙[√( 1 + 16∙1/0.49) - 1] = 0.294 atm => P = p₀ + x = 1 atm + 0.294 atm = 1.294 atm