仁川機場去東大門區

長漢砰站 is not in 東大門區 and it's at the east side of 東大門.
If you take the airport subway from 仁川機場 to 金甫機場 and then change to subway line 5 (purple), you may go to 長漢砰站장한평역 direct. It's the 31st station (station number 543) down subway line 5. The whole journey is around 1.5 hour.