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.

# Answer

180
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Samuel is arranging his grandma’s teacups. They are stored in boxes and inside the boxes, they are stacked 5 rows high with 4 cups in each row. Of the 26 boxes in her attic, 6 of the boxes contain pans, half of the remaining boxes contain decorations, and the rest of the boxes contain her teacups. Samuel breaks 2 of the cups every time he picks up one of the boxes. By the time Samuel has taken all of the teacups out of the boxes, how many teacups are left?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
180
Samuel is arranging his grandma’s teacups. They are stored in boxes and inside the boxes, they are stacked 5 rows high with 4 cups in each row. Of the 26 boxes in her attic, 6 of the boxes contain pans, half of the remaining boxes contain decorations, and the rest of the boxes contain her teacups. Samuel breaks 2 of the cups every time he picks up one of the boxes. By the time Samuel has taken all of the teacups out of the boxes, how many teacups are left?
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