The 6 triangles have 3 sides each, for a total of 6 * 3 = <<6*3=18>>18 sides.
The 4 squares have 4 sides each, for a total of 4 * 4 = <<4*4=16>>16 sides.
The 2 hexagons have 6 sides each, for a total of 2 * 6 = <<2*6=12>>12 sides.
The total numbers of sides is 18 + 16 + 12 = <<18+16+12=46>>46 sides.
#### 46