$A = \begin{bmatrix}
2 & b\\
4 & 8
\end{bmatrix}$
and let the augmented matrix be
$A|B = \begin{bmatrix}
2 & b & 16\\
4 & 8 & g
\end{bmatrix}$
For singularity, $|A| = 0$ but this says that the system of linear equations can have either no solution or infinite solution .
We get $b=4$
Now, since to make it solvable i.e. having infinite solutions, we need to make the last row of augmented matrix = $0$.
Now, this is only possible if we take $g=32$, then last row completely gets eliminated and hence, we have infinite solutions .