Answer
$x = 41.2~m$
Work Step by Step
We can find the path length difference when the phase difference is $1.50~\lambda$:
$1.50~\lambda = (1.50)(2.00~m) = 3.00~m$
We can form a right angle triangle with sides of length $d$, $x$, and $x+3.00$
We can find $x$:
$x^2+d^2 = (x+3.00)^2$
$x^2+d^2 = x^2+6.00~x+9.00$
$d^2 = 6.00~x+9.00$
$6.00~x = d^2-9.00$
$x = \frac{d^2-9.00}{6.00}$
$x = \frac{(16.0)^2-9.00}{6.00}$
$x = 41.2~m$
