$$ \begin{align} \ce{PbO2 + H2SO4 &-> PbSO4 + H2O + O} &\quad &\text{(anode)}\\ \ce{Pb + H2SO4 &-> PbSO4 + H2} &\quad &\text{(cathode)} \end{align} $$
The cathode’s $\ce{H2}$ joins the anode’s $\ce{O}$ making $\ce{H2O}$ in solution. The book says the cathode gets four electrons, but from where? Two liberated hydrogens have one each, that’s two. Where’d the other two come from?