OK, it seems to me that what you have is a fits image (from where?) that has some world coordinate system information attached. When you load the 2MASS catalogue, SAOimage is able to use the RA and Dec in the catalogue to calculate the x,y positions of the catalog sources in your image (and marks them as green circles).
Is what you are asking - how do I get the x,y coordinates of these 2MASS sources in my image? Or do you wish to know what the x,y coordinates of the actual sources in your image? If the latter then you will need some other software like Sextractor or DAOphot to do source-searching and parameterisation in your image.
If the former, here's a way of doing it. When you load the catalog you should see a window open entitled "2MASS Point sources" which lists all the sources in your image. From the "File" dialogue, select "Copy to regions". Then, in the main image window open the "Regions" dialogue and select "List regions". Another dialogue box will open asking you to select the format and coordinate system. From this, select "x,y" for the format and "image" for the coordinate system. This will give you a list of x,y coordinates.
If you want to match this up with the 2MASS sources then you have to "list regions" again, but this time select "fk5" as the coordinate system. This will then give you a list of the RA, Dec of the same sources. Use you favourite editor to attach these lists to each other.
Quite probably there is a more elegant solution, but this works.