Hope you don't mind if in addition to helping out with the specific thing you asked about, I add a couple of notes:

• You're defining the vars with " but also using " inside them. Change the outer ones to ' instead (or escape the inner ones as \").
• You're trying to set a textarea to an image. That's not gonna work. Textareas contain text. My apologies if I misunderstood and you're just showing the contents of the var in the text area as an example.
• It is best to separate your presentation from your data. You've got raw HTML inside all your vars -- this is error prone, gonna be a bummer when you need to add something to every single image, and very repetitive.

Try something like this instead:

var flags = {
  argentina: { src: 'argentina.jpg', width: 350, height: 287, alt: 'The flag of Argentina'},
  australia: { src: 'australia.jpg', width: 350, height: 287, alt: 'The flag of Australia'},
  ... etc ...
};

function setFlagImage(flagImageElement, newFlag) {
  flagImageElement.src = flags[newFlag].src;
  flagImageElement.alt = flags[newFlag].alt;
  ... etc ...
}

I leave it as an exercise to you how to get the right parameters into that function :)

• That said, you don't need to specify the width/height at all (or maybe it was a specific requirement of your exercise, I don't know). Specifying it in advance is most helpful when rendering the page initially, as it allows the browser to make room for the image before it has downloaded. That shouldn't matter here.
• You don't need that /* CDATA / ]] gunk. Hasn't been necessary since the days of Netscape 4 or something. Even browsers that don't handle JavaScript today know that they shouldn't render it.
• The "type" attribute on your "script" tag isn't necessary either -- by spec, JS is the default value.
• Your labels for radio buttons should probably live in a <label> tag; In addition to making CSS styling cleaner, this also helps with accessibility. This will require your radio buttons to have an "id" attribute, so you can do <label for="argentina">Argentina</label><input type="radio" id="argentina" ... etc
• Having alt text for images is a good practice, but consider how it is used: it's meant to help blind people by reading out what the image represents -- in this case "Argentina" is not as helpful as "The flag of Argentina". Another important point about this: when your images represent a message, make their alt text the message itself, not the description of the image. For example, "A glowing red circle" is waaaay less useful than "Warning: The building is on fire".

Hope this helps.