Four, (Full marks 15 points) The unit digit of an $n$-digit number is 6. Moving the 6 to the front of the number while keeping the other digits in place results in a new $n$-digit number, which is 4 times the original $n$-digit number. Find the smallest positive number that satisfies the above conditions.

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 untranslated text:
(满分 15 分) 某 $n$ 位数的个位数字是 6 , 将 6 移到该数的首位、其余各位数字不动, 得到新的一个 $n$ 位数, 这个新数髶原 $n$ 位数的 4 倍, 求出满唗上述条件的最小正数。

translated text:
(Full marks 15 points) The unit digit of an $n$-digit number is 6. Moving the 6 to the front of the number while keeping the other digits in place results in a new $n$-digit number, which is 4 times the original $n$-digit number. Find the smallest positive number that satisfies the above conditions.
From the problem, we know that the first digit must be 1.
Expression:
$$
\begin{array}{r}
1 \cdots E D C B A 6 \\
\hline 6 \cdots E D C B A
\end{array}
$$

We get $A=4, B=8, C=3, D=5, F=1$. $\therefore$ The smallest number is 15384.