Compressing a gaseous system raises every partial pressure, and the system responds by shifting toward whichever side has fewer moles of gas. Expanding does the opposite. If both sides have equal moles of gas, changing the volume causes no shift at all.
For N₂O₄ ⇌ 2 NO₂, Qp = PNO₂²/PN₂O₄. Halving volume at fixed T initially doubles each partial pressure, so Qnew = (2²/2)Qold = 2 K. Since Q > K, the reaction shifts toward N₂O₄, the side with fewer gas moles. More generally, multiplying all gas partial pressures by f multiplies Q by fΔn. If Δn = 0, the factors cancel. The fewer-moles rule concerns a pressure change caused by compression, not any increase in total pressure from any cause.