Answer
The charge transfer through the wire will be $-2e$
Work Step by Step
Let $q$ be the initial charge of each bubble.
After bubble A hits the ceiling, the charge on bubble A is zero.
After bubble A hits bubble B, both bubbles have the same charge.
The charge on bubble A and bubble B is $\frac{q}{2}$
In part (a), we found that the initial charge of each bubble was $~~+4e$
Then the charge on bubble A when it hits the floor is $+2e$
Therefore, the charge transfer through the wire will be $-2e$
