||] X here is: -73918033, the Y is 40844593.
I agree with Paul. If you can ask the other company to provide the data
with changes, ask them to do two things.
1) Format the xy values as decimal degrees. ex. -73.918033 40.844593
otherwise, you'll have to do it before you can import it into ArcMap.
2) Ask them to confirm the coordinate system as NAD83 or WGS84 or
something else. It's almost certainly one of these, but better to be sure!
Once you can get this data imported, you can project it on-the-fly to
the Long Island coordinate system.