Answer
$$x=0, \quad y=2-4t, \quad z= t.$$
Work Step by Step
The augmented matrix is given by
$$\left[ \begin {array}{cccc} 3&3&12&6\\ 1&1&4&2
\\ 2&5&20&10\\ -1&2&8&4
\end {array} \right]
.
$$
Adding the first row to $-3$ times the second row, adding $-2$ times the first row to $3$ times the third row, adding the first row to $3$ times the fourth row, we get
$$\left[ \begin {array}{cccc} 3&3&12&6\\ 0&3&12&6
\\ 0&0&0&0\\ 0&0&0&0\end {array}
\right].
$$
Now, the crossposting system is given by
$$
\begin{align*}
3x+3y+12z&=6 \\
3y+12z&=6.
\end{align*}
$$
The above system has the solution
$$x=0, \quad y=2-4t, \quad z= t.$$
