You don't need partial pressures to answer that question in the sense of a detailed explanation, calculation or formula written version of it that's taught in 1st year university chemistry where you learn about Ptotal = P1 + P2 + P3 + .... + Pn. It's more you need to memorise a certain phrase or concept around the things when added to an equilibrium don't cause it to shift which are:
1. Catalyst - it just speeds up the how fast the equilibrium is reached since it increases rate of reaction but it doesn't cause a shift
2. Solids - when added to a saturated solution have no effect cause you already reached the max solubility so you can't dissolve any more to change the concentration of things involved in a reaction
3. Inert gases - like helium and argon. It increases overall pressure of the system but it doesn't change the partial pressures (or simply put the amount of the reactants/products)
That last 3rd thing is basically the key point they want you to write about.
An answer to this question would be along these lines:
- Mention that adding an inert gas increases overall pressure of the system but it doesn't change the amounts of the NO2 and N2O4 present and the volume of the vessel doesn't change either since it says in the question its a fixed volume vessel(you can use the words partial pressures here if you want to but it wouldn't lead to you losing marks if you didn't because saying it doesn't change amounts of NO2 and N2O4 is essentially the same thing)
- Link this then to this means there is no shift in the position of the equilibrium based on Le Chatelier's principle since there is no disturbance and therefore no resulting change in the NO2 and N2O4 concentrations
- Now link it to temperature in that because the equilibrium was not disturbed the rate of the exothermic forward reaction = rate of the endothermic reverse reaction. That means the system is in dynamic equilibrium where changes are happening on a microscopic level but there's no total change to things like temperature.
- You can mention things like K constant doesn't change as well if you want
I do agree though with what was posted earlier about it's a bit strange this question is 4 marks. As someone who is an experienced tutor if I was making this question I would make it max 3 marks.