.. How do I open the number wheel in the dresser?

This will take you quite a while, so settle in. It all hinges on following up the journal in the desk here --

How do I open the desk?

-- and tracking down those soundings.

What am I doing with the soundings map?

When you have all four numbers, come back to this lock, and Nancy will say --

-- that you need to enter all four numbers, from the smallest to the largest. In case you forget, the numbers are 11, 14, 26, and 35. (But they won't work until you find them on the soundings map.)

Enter the smallest number, and one of the four pieces in the center will pop out. When all four pieces pop out --

-- go down into the ship's hold to find out what just happened.

Ship's Hold