You need to work out the area of each face:
Purple: 1 x 4 + 5 x 2 (double it as we have the front and back)
Red: 3 x 2 + 3 x 2 (double it as we have two sides)
Green: 1 x 3 + 5x 3 (double it as we have the top and bottom)
Then add the 3 answers together.