To convert a number from base \(e\) to base \(7\), you can first convert it to base \(10\) and then from base \(10\) to base \(7\).

Given \(12_{e}\), where \(e = 12\), we need to convert it to base \(10\):

\(12_{e} = 1 \times 12^1 + 2 \times 12^0 = 12 + 2 = 14_{10}\)

Now, we need to convert \(14_{10}\) to base \(7\):

Divide \(14\) by \(7\):
\[14 = 2 \times 7 + 0\]

So, in base \(7\), \(14_{10}\) becomes \(20_{7}\).