Answer
If the two currents are doubled, the zero-field point is unchanged.
Work Step by Step
Suppose the both currents are doubled. Note that the value of $i_2$ is still equal to $3.00~i_1$
If the net magnetic field is zero, the magnetic field due to each current must be equal in magnitude and opposite in direction. By the right hand rule, this point must be somewhere between the two currents.
Let $x$ be the point where the net magnetic field is zero. Then the distance from $i_2$ is $~~(16.0~cm-x)$
We can write the general expression for the magnetic field produced by a current in a straight wire:
$B = \frac{\mu_0~i}{2~\pi~R}$
To find $x$, we can equate the magnitude of the magnetic field due to each current:
$\frac{\mu_0~i_1}{2~\pi~x} = \frac{\mu_0~i_2}{(2~\pi)~(0.160-x)}$
$\frac{i_1}{x} = \frac{3.00~i_1}{0.160-x}$
$\frac{1}{x} = \frac{3.00}{0.160-x}$
$0.160-x = 3.00~x$
$4.00~x = 0.160$
$x = 0.0400~m$
$x = 4.00~cm$
At $~~x = 4.00~cm~~$ the net magnetic field is zero.
If the two currents are doubled, the zero-field point is unchanged because the value of $i_2$ is still equal to $3.00~i_1$
