Drawing the background is actually quite easy. The "fillRect" command associated with the pen will fill the whole background of the applet screen region for you if you just omit the first four parameters usually used to specify the location and size of the rectangle to be filled. The only trick is you have to get the color right.
You can't just type in a color name (like "Red") for the background color. The color to be used has to be "mixed" using a "new Color(...)" constructor. As you type in the program, however, the numbers to use for the red, green and blue value parameters expected by the "new Color(...)" constructor aren't known. They will have to vary as the applet runs to reflect the setting of the scrollbars.
That is why we had you define your drawing method to expect the three color numbers as parameters. Within the drawing method you can use the parameter names as placeholders for the numbers that correspond to the scrollbar setting.
So, add to your drawing method's body an invocation of the pen's "fillRect" method that will paint the background in the color corresponding to the parameter values.
To see if you got it right, you should run your applet. Try it, and once you fix any typing or grammatical errors in your program you will discover that all that appear are the three scollbars you added earlier. The reason for this is simple. By defining your drawing method you have told the computer what to do if it ever is told to redraw the background, but you never told it when it actually needs to do this.
As we said earlier, one of the places it needs to do this is in the "begin" method. So, you should add a line to the body of your begin method after the lines that add the scrollbars to actually invoke your method to draw the background.
In your background drawing method's heading you indicated to Java that the method would expect three parameters. As a result, Java won't let you invoke the method unless you provide three numbers it can use to use in place of the "placeholder" parameter names while following the instruction(s) within your background drawing method. Eventually, the value you would like to use should come from the scrollbars. We don't want to get into that yet. So, at the end of your "begin" method add an invocation of your drawing method with parameters like "200, 0, 200". Then, run your applet. Once it works it should display a nice purple background.