The work done by the battery is equal to the charge transferred during the process times the potential difference between the two terminals of the battery:
[tex]W=q \Delta V[/tex]
where q is the charge and [tex]\Delta V[/tex] is the potential difference.
In our problem, the work done is W=39 J while the potential difference of the battery is [tex]\Delta V = 9.0 V[/tex], so we can find the charge transferred by the battery:
[tex]q= \frac{W}{\Delta V}= \frac{39 J}{9.0 V}=4.33 C [/tex]
