Air carrier pilot reported a ground conflict after being cleared to taxi to departure runway. Pilot stopped taxi after realizing that landing traffic was about to land on a runway the reporter had been cleared to cross.

Narrative

While holding short of runway 22R at HNL; we were cleared; by Tower Control to cross Runway 22R and 22L and to hold short of Runway 26R on taxiway C. I read back the clearance to Tower.The CA confirmed the clearance and we checked the final. The CA (Captain) had a better view than I did; looking left. Final appeared clear and the CA began taxiing. As we were making our way across RWY 22R; the CA said he could see an aircraft on final; but wasn't sure which runway it was lined up for or how far out it was. The CA mentioned that he had heard Aircraft Y given landing clearance; but he did not see them or know how far out they were. I looked and did not see an aircraft initially and then within seconds; noticed Aircraft Y on final. It appeared to be landing on runway 22L; which we had not yet crossed. The CA decided to stop just barely short of the hold short line for runway 22L. Within seconds; Aircraft Y passed in front of us but high; and landed on runway 22L. Had we continued; Aircraft Y would have likely passed over us while we were in the middle of runway 22L prior to landing on 22L. I queried Tower that we were cleared across runway 22R/22L but we saw Aircraft Y pass in front of us. The controller said; ''roger; continue C short of RWY 26R'' We complied and continued the flight with no further incident. The controller sounded very busy as they were working multiple types of traffic to multiple runways; vfr; ifr; large; mid; small TO; LDG; ETC.