If it's aimed at a young enough audience, it might be better to present multiple choice buttons instead of a text field, so that could be the "real" answer to the problem... but it might not solve the overall issue of "where do I get started / how do I even think about the problem?"
As for how you do what you've asked about, it looks like you have 4 or 5 pre-defined colors, so that makes it easier. I'm not going to talk about how to tween the paint buckets, many of the specifics of how to structure anything or how to get the "wrong/correct" text onto the screen, only give a rough overview of what you'd do for the main game logic.
First thing you would do is create an array of color names so that you can select the color you need.
Code:
var colorNames:Array = ["red","blue","green","orange"];
Then you'd make an array containing the paint buckets of the same color that you'd use to select the paint bucket image you need.
Code:
var buckets:Array = [redBucket,blueBucket, ...];
Now in order to make a selection from the Array you need a random number generator. Flash has a way to get a random number. Call Math.random() to recieve a number between 0 and 1. Multiply this by the number of items in your array and round down. You now have a random number pointing to an array location. Store the currently selected color into a variable:
Code:
var randomNumber:int = Math.floor(Math.random() * colorNames.length);
var currentColor:String = colorNames[randomNumber];
Bring the selected paint bucket onscreen.
When the user presses the "ok" button, you'll want to compare the value of the text field against the current word. If you don't care what kind of capitalization the user types, you can use "toLower()" to change the value of the text box. That way a user typing "OrANge" will still be correct if the array value as "orange"
Code:
if(textField.text && textField.text.toLower() == currentColor){
// You win!
}else{
// wrong!
}
This is of course an incredibly rough overview. There are a lot of holes you'll have to fill in yourself. Also, this does not go into any of the more advanced topics of Object Oriented Programming.