We form the augmented matrix of the homogeneous system $\linearsystem{B}{\zerovector}$ and row-reduce the matrix,
\begin{align*}
\begin{bmatrix}
-6 & 4 & -36 & 6 & 0 \\
2 & -1 & 10 & -1 & 0 \\
-3 & 2 & -18 & 3 & 0
\end{bmatrix}
&\rref
\begin{bmatrix}
\leading{1} & 0 & 2 & 1 & 0 \\
0 & \leading{1} & -6 & 3 & 0 \\
0 & 0 & 0 & 0 & 0
\end{bmatrix}
\end{align*}
We knew ahead of time that this system would be consistent (Theorem HSC), but we can now see there are $n-r=4-2=2$ free variables, namely $x_3$ and $x_4$ (Theorem FVCS). Based on this analysis, we can rearrange the equations associated with each nonzero row of the reduced row-echelon form into an expression for the lone dependent variable as a function of the free variables. We arrive at the solution set to the homogeneous system, which is the null space of the matrix by Definition NSM,
\begin{align*}
\nsp{B}=\setparts{\colvector{-2x_3-x_4\\6x_3-3x_4\\x_3\\x_4}}{x_3,\,x_4\in\complexes}
\end{align*}