The first step that I would take is to lay out the number of ways to put the balls into the boxes, regardless of uniqueness of the balls.
One way is to have 2 in a box, 1 in a box, and 1 in the last box. Are there any other ways?
After we know the ways to arrange the balls, it is time to factor in uniqueness. One arrangement for the balls is 2 in a box, 1 in a box, and 1 in a box. So how many ways can you arrange unique balls in this type of array? Using Khan's method of labeling the color of balls, one way would be to put blue and green in a box, red in a box, and yellow in the last box. How many arrangements for this scenario are there?