Hi Ditto - yes usually you want to use the Offset command to create a curve that is a constant thickness away from an existing one.
Over here when I use the Offset command on your curve, it seems to work fine... But note that your curve is a planar curve in the Front view - that means that to use Offset you will need to pick a point in that Front view to produce the offset.
My guess is that you were possibly trying to go to the Top view to produce the offset? Going to the Top view will not produce any result with Offset, because Offset is going to try to produce an offset curve within the same plane as the existing curve, and when you go the Top view that is looking directly down at the edge of that plane.
Just to illustrate more, Offset will produce results like this (seen here in the Front view):
I suspect that what you may want is actually just a copy of the curve, positioned at a certain distance away from it in the Top view, instead of the kind of result that Offset makes? If so to do that, select the curve and run the Transform > Copy command. Pick the base point somewhere (doesn't actually matter exactly where, but somewhere on the curve is convenient), and then for the target point of the copy if you want to place it a specific distance away enter that distance value to activate "distance constraint" and then the copy will use that specific displacement from the base point.
Like for instance if you want to make a copy exactly 5 units away, select the curve, run the Transform > Copy command, click the base point on the curve, then type in 5 and push enter to activate distance constraint, now when you move the mouse to place your target point you will be picking a displacement of 5 units for placing the copy.
When picking the second point to be copied, make sure "Straight Snap" is enabled if you want to place the copy displaced along an axis direction - when straight snap is enabled you will get directional snaps along the x and y axis in any command that picks 2 points in sequence like Copy or drawing lines, etc...
Please let me know if the Copy command does not do what you need or if you're still stuck.
- Michael