solution: If $n \equiv 2 \pmod{7}$, then $(n + 2)(n + 4)(n + 6) \equiv 4 \cdot 6 \cdot 8 \equiv 4 \cdot 6 \cdot 1 \equiv 24 \equiv \boxed{3} \pmod{7}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  If $n \equiv 2 \pmod{7}$, then find the remainder when $(n + 2)(n + 4)(n + 6)$ is divided by 7.
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 3
extra_info.question: If $n \equiv 2 \pmod{7}$, then find the remainder when $(n + 2)(n + 4)(n + 6)$ is divided by 7.
extra_info.split: test