Answer
$-1344$
Work Step by Step
Multiplying the first row by $-3$ and adding it to the third row. Also, adding the first row to the fourth row, we get
$$\left|\begin {array}{cccc} 4&-7&9&1\\ 6&2&7&0
\\ -9&27&-30&0\\ 4&0&13&0\end {array}
\right|.$$
Expanding by cofactors using the fourth column, we get
$$\left|\begin {array}{cccc} 4&-7&9&1\\ 6&2&7&0
\\ -9&27&-30&0\\ 4&0&13&0\end {array}
\right|=-\left|\begin {array}{cccc} 6&2&7
\\ -9&27&-30\\ 4&0&13\end {array}
\right|=-(-2)\left|\begin {array}{cccc}
-9& -30\\ 4& 13\end {array}
\right|-27\left|\begin {array}{cccc}
6& 7\\ 4& 13\end {array}
\right|=2(-117+120)-27(78-28)=6-1350=-1344.$$
