Solution: 14 different ways.

We can count in an organized way.  First we put one crayon in the star box and the other 3 in the circle box. This gives us a total of 4 ways.  Next we put 2 crayons in each box. This gives us a total of 6 ways. Finally we put 3 crayons in the star box and 1 crayon in circle box.  This gives us a total of 4 ways.

In all, there are 4 + 6 + 4 = 14 different ways to put the crayons in the boxes.