(a) Consider a conductor of length $L$ and cross-sectional area $A$ carrying current $I$. Let $n$ be the number of free electrons per unit volume and $v_d$ the drift velocity. In time $\Delta t$, electrons travel a distance $v_d\Delta t$. The volume swept is $A v_d\Delta t$, containing $nAv_d\Delta t$ electrons. Charge crossing a section in time $\Delta t$: $$\Delta q = (nAv_d\Delta t)e$$ Current: $$I = \frac{\Delta q}{\Delta t} = neAv_d$$ This is the required relation. (b) Drift velocity is related to the applied field by $v_d = \dfrac{eE\tau}{m} = \dfrac{eV\tau}{mL}$. At constant voltage $V$, if the length $L$ is doubled, then $E = V/L$ becomes half, so $v_d$ becomes half its original value. Hence doubling the length (at constant voltage) reduces the drift velocity to one-half.