Given that $\begin{vmatrix} a & b \\ c & d \end{vmatrix} = 6$ and $\begin{vmatrix} a & b \\ c & d \end{vmatrix} = 3$, find the value of $\frac{\begin{vmatrix} 2a & b \\ 2c & d \end{vmatrix}}{\begin{vmatrix} a & 2b \\ c & 2d \end{vmatrix}}$ as a percentage. Let's think step by step and output the final answer within \boxed{}.
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