Answer
The x-coordinate is increasing at a rate of $6~cm/s$
Work Step by Step
We can differentiate both sides of the equation with respect to $t$:
$xy = 8$
$y~\frac{dx}{dt}+x~\frac{dy}{dt} = 0$
$y~\frac{dx}{dt} = -x~\frac{dy}{dt}$
$\frac{dx}{dt} = -\frac{x}{y}~\frac{dy}{dt}$
$\frac{dx}{dt} = (-\frac{4}{2})~(-3~cm/s)$
$\frac{dx}{dt} = 6~cm/s$
The x-coordinate is increasing at a rate of $6~cm/s$.