The drift velocity of electrons in a metal is given by:

\(v=\frac1{enA}\)

Where,

I = current,
n = electronic concentration,
e = electronic charge,
A = area of the cross-section.

Now,

\(A=\frac{\pi d^2}4\)

When the diameter is halved, a new area of cross-section is 

\(A'=\frac{\pi\left({\displaystyle\frac d{}}\right)^2}4=\frac14\frac{\pi d^2}4=\frac A4\)

Then new drift velocity is given as

\(v'=\frac1{en{\displaystyle\frac A4}}=4v\)

∴ v' = 4v, the drift velocity increases 4 times when the diameter of wire is halved.