Answer
The new charge of the sphere is $~2.7~nC$
The new charge of the rod is $~-4.7~nC$
Work Step by Step
We can assume that the electrons are transferred from the negatively charged rod to the positively charged sphere.
We can find the charge of $8.2\times 10^9$ electrons:
$q = (8.2\times 10^9)(-1.6\times 10^{-19}~C)$
$q = -1.3\times 10^{-9}~C$
$q = -1.3~nC$
The new charge of the sphere is $4.0~nC-1.3~nC$ which is $2.7~nC$
The new charge of the rod is $-6.0~nC-(-1.3~nC)$ which is $-4.7~nC$
