Chinese means 4 red and 6 white 10 blue. Take a ball at random at a time and ask how many balls you need at least to make sure it contains 2 reds, 2 whites and 2 blues.

This is my idea. Consider extreme cases:

The front 10 is blue. 10 has been shot, and two blue ones have been completed.

Take two more, both white. 12 pieces have been taken, 2 pieces are blue and 2 pieces are white.

Take two more, still white. 14 pieces have been taken, 2 pieces in blue and 2 pieces in white.

Take two more, still white. 16 pieces have been taken, 2 pieces are blue and 2 pieces are white.

Two more shots. Well, it's finally popular. 18 pieces have been shot, 2 pieces in blue, 2 pieces in white and 2 pieces in red.

So the answer is e.