Answer
$x = 128~m$
Work Step by Step
We can find the path length difference when the phase difference is $0.5~\lambda$:
$0.5~\lambda = (0.5)(2.00~m) = 1.00~m$
We can form a right angle triangle with sides of length $d$, $x$, and $x+1.00$
We can find $x$:
$x^2+d^2 = (x+1.00)^2$
$x^2+d^2 = x^2+2.00~x+1.00$
$d^2 = 2.00~x+1.00$
$2.00~x = d^2-1.00$
$x = \frac{d^2-1.00}{2.00}$
$x = \frac{(16.0)^2-1.00}{2.00}$
$x = 128~m$
