Bài giải:

$\begin{align}

  & 3\frac{1}{11}\times \frac{27}{46}\times 1\frac{6}{17}\times 2\frac{4}{9} \\

 & =\frac{34}{11}\times \frac{27}{46}\times \frac{23}{17}\times \frac{22}{9} \\

 & =\frac{(17\times 2)\times (9\times 3)\times 23\times (11\times 2)}{11\times (23\times 2)\times 17\times 9} \\

 & =\frac{(11\times 23\times 2\times 17\times 9)\times 2\times 3}{11\times 23\times 2\times 17\times 9} \\

 & =2\times 3 \\

 & =6 \\

\end{align}$