Breaking down the equation

n is the number density of charge carriers, which is the number of charge carriers per unit volume of the material, typically measured in m⁻³.
A is the cross-sectional area of the conductor, measured in square meters (m²).
q represents the charge of each charge carrier, measured in coulombs (C). For electrons, this is the elementary charge e, where e = 1.6 × 10⁻¹⁹ C.
v is the average drift velocity of the charge carriers, measured in meters per second (m s⁻¹).
Note: Average drift velocity is merely the speed at which one charge carrier moves from one end of the conductor to the other, given by the equation \( l/t \). The actual speed is a lot higher but the charge carriers bounce around as they move through the conductor, making their path longer.

What happens when A changes?

The current (I) in a conductor always remains the same no matter what happens.
If the cross-sectional area of the conductor is reduced by half (A becomes A/2), the equation becomes \( I = n \left( \frac{A}{2} \right) v_2 q \).
I remains the same. As n and q are constant, v increases. Thus, the equation becomes:
\( nAv_1q = n(A/2)v_2q \)
The terms n, A and q can be cancelled, giving \( v_1 = \frac{v_2}{2} \). Thus, \( v_2 = 2v_1 \).