Taking the boxes of pans out of the total attic boxes shows that 26 boxes – 6 boxes of pans = 20 boxes are either decorations or teacups.
Since half of these boxes are decorations, the other half must be made up of 20 boxes / 2 = <<20/2=10>>10 boxes of teacups.
Each box of cups initially has 5 rows x 4 cups = <<5*4=20>>20 teacups inside.
Samuel breaks cups each time he picks up a box, which means each box now contains 20 – 2 = <<20-2=18>>18 teacups.
Therefore, there are 10 boxes * 18 teacups = <<10*18=180>>180 teacups left.
#### 180