solution: Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of the fraction.  The reciprocal of $\frac{2}{3}$ is $\boxed{\frac{3}{2}}$, so that is what Remmy should multiply by.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Remmy wants to divide $10$ by $\frac{2}{3}$, but he cannot remember how to do that.  By what number should he multiply $10$ to get the answer?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: \frac{3}{2}
extra_info.question: Remmy wants to divide $10$ by $\frac{2}{3}$, but he cannot remember how to do that.  By what number should he multiply $10$ to get the answer?
extra_info.split: test