From the time you enter the ducts, follow these directions. F=forward, L=left, R=right.

F-F-F-F-L F-F-R F-L F-F-L F-F-R F-F-R F-F-L F-F-F-R F-F-R F-F-L F-F

At the end, there's a second square opening in the floor; approach it to overhear a conversation and then drop down into the hall.