Answer
The net emf is $~~23.48~V$
Work Step by Step
We can find the induced emf:
$\mathscr{E} = -A~\frac{dB}{dt}$
$\mathscr{E} = -(2.00\times2.00~m^2)~(-0.870~T/s)$
$\mathscr{E} = 3.48~V$
The magnetic flux out of the page is decreasing. By Lenz's law, the induced current opposes this change. By the right hand rule, the induced current is counterclockwise. Then, the induced emf is counterclockwise, which is the same direction as the battery emf.
We can find the net emf:
$\mathscr{E}_{net} = 20.0~V+3.48~V = 23.48~V$
The net emf is $~~23.48~V$
