Answer
$abgd$
Work Step by Step
First, use cofactor expansion (Theorem 4.1) along the third row because that is the row/column with the most zeros:
\[
\begin{vmatrix}
0 & 0 & 0 & a\\0 & 0 & b & c\\0 & d & e & f\\g & h & i & j
\end{vmatrix}
=
0-0+0-a \cdot
\begin{vmatrix}
0 & 0 & b\\0 & d & e\\g & h & i
\end{vmatrix}
\]
Now expand along the first row again:
=$-a \cdot (0-0+b \cdot
\begin{vmatrix}
0 & d\\g & h
\end{vmatrix}
)$
Lastly, simplify the expansion:
$=-a \cdot (b \cdot (0-gd))$
$=abgd$
