The total pressure after equilibrium will be 0.854 atm calculated  help of kp.Since the Kp depends on the individual partial pressures of the components in mixture.
Nâ‚‚Oâ‚„ ==> 2NOâ‚‚
initial..0.554.........0
change....-p..........+2p
equil....0.554-p.......2p
Total Pressure at equilibrium  = 0.770;
therefore,
0.554-p+2p = 0.770 and this allows  to calculate Kp.
NO₂ is injected to make  the Ptotal equals to 0.906 bar
so that makes 0.906-0.770 = 0.136 bar  being injected.
It would make a new ICE chart with the NO₂ start = 0.136 + old equilibrium pressure of  N₂O₄ = old equilibrium and recalculate the new pressures using the Kp from the first part. You know of course that the reaction will be shifted to  left side
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