solution: The hexagon has a side length of 16 centimeters, so its perimeter is $16\times 6 = 96$ centimeters. Since the octagon and the hexagon have the same perimeter, it follows that each side of the octagon has a length of $96/8 = \boxed{12}$ centimeters.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  A regular octagon has the same perimeter as the regular hexagon shown here with side length 16 cm.  How long is each side of the octagon? [asy]size(80); pair A = dir(120); pair B=dir(60); pair M=(A+B)/2; draw(dir(360)--B--A--dir(180)--dir(240)--dir(300)--cycle); label("16 cm", M, N);[/asy]
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 12
extra_info.question: A regular octagon has the same perimeter as the regular hexagon shown here with side length 16 cm.  How long is each side of the octagon? [asy]size(80); pair A = dir(120); pair B=dir(60); pair M=(A+B)/2; draw(dir(360)--B--A--dir(180)--dir(240)--dir(300)--cycle); label("16 cm", M, N);[/asy]
extra_info.split: test