Solution:
Let the required number of machine be x
More persons, More machines (Direct proportion)
More working working hours, More machines (Direct proportion)
More days, More machines (Direct proportion)
\[\left. \begin{gathered}
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Persons 2}}:6 \hfill \\
\,\,\,\, {\text{Working hours 2}}:6 \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 2}}:{\text{6}} \hfill \\
\end{gathered} \right\}::2:x\]
$$\eqalign{
& \therefore {\text{ }}2 \times 2 \times 2 \times x = 6 \times 6 \times 6 \times 2 \cr
& \Leftrightarrow x = \frac{{\left( {6 \times 6 \times 6 \times 2} \right)}}{{\left( {2 \times 2 \times 2} \right)}} \cr
& \Leftrightarrow x = 54 \cr} $$