Answer
$ V_a -V_b = 12V - 4V = 8V$
Work Step by Step
when switch is open
$3\Omega $ and $3\Omega $ are in series and $5\Omega $ and $1\Omega $ are in series. Both these combinations are in parallel with each other.
$\frac{1}{R_{eq}} = \frac{1}{3+3} +\frac{1}{5+1}$
$R_{eq} =3\Omega $
Now $I =\frac{24}{3} A= 8A$
$4A$ will flow through both combinations as both have net resistance same so half half current will flow through each.
potential at a
$V_a = 24V - 4A* 3\Omega = 12V$
potential at b
$V_b = 24V - 4A*5\Omega = 4V$
potential difference
$ V_a -V_b = 12V - 4V = 8V$
