find vector same direction as .. but has length ..

Hi having trouble understanding this. Question asks find the vector that has same direction as -2i+4j+2k but that has length 6.

To get the unit vector is did this.

$\displaystyle

\begin{array}{l}

\hat u = \frac{v}{{||v||}} \\

= \frac{1}{{\sqrt {24} }} < - 2,4,2 > \\

= \frac{1}{{2\sqrt 6 }} < - 2,4,2 > \\

\end{array}

$

Then to find the vector in that direction but length 6, I thought you just multiplied the unit vector by 6. So I get this

$\displaystyle

\begin{array}{l}

= \frac{6}{{2\sqrt 6 }} < 2,4,2 > \\

= 3\sqrt 6 < 2,4,2 > \\

\end{array}

$

But the answer is

$\displaystyle

\sqrt 6 < - 1,2,1 >

$