Im making a simple coloring map but how would I use actionscript to save the map after coloring it so that after opening it again its the color i last used

When you create an swf file using Flash what you end up with is a file that cannot be permanently altered in any manner.  If you want to make that file capable of remembering a previous state then you have to build that kind of intelligence into the file.  The file will need to store the information it needs in some external data receptacle (database, data file, text file, cookie) and when you open the file it would need to automatically check for that data when it opens.  So the flow of processing would be something like...

run the file -> file loads data from its data resource -> file adjusts itself per that data -> you change the map in some way and the file collects the change information for storage into the data file -> something triggers the file to save its current data -> close the file.

For the most part, Flash is not capable of saving data to a file or a database without the use of a server-side processing program... often a PHP processing file is used for this...  it acts a s ago between for Flash and the data resource.

Flash does have the ability to store data in what is considered the Flash version of a cookie - called a shared object.  HEre is a link to get some info about it...  Flash Cookies explained - gHacks Tech News