Since both pieces of ribbon are of the same length, find the common multiple of 40 and 180 first.
9 x 40 = 360
2 x 180 = 360

For every 360 cm,
9 x 3 = 27 smiley stickers
2 x 9 = 18 star stickers
Therefore there are 9 more smiley stickers than star stickers for every 360 cm of ribbon.

216 / 9 = 24 
24 x 360 = 8640 cm
Each ribbon is 8640 cm long.

Number of smiley stickers = 8640 / 40 x 3 = 648
Number of star stickers = 8640 / 180 x 9 = 432
Total number of stickers = 648 + 432 = 1080