Answer
The magnitude of their gravitational force of attraction is $\frac{G~M^2}{4R^2}$.
Work Step by Step
We can use Newton's law of gravitation to find the magnitude of their gravitational force of attraction. Note that the distance between their centers is 2R.
$F = \frac{G~M~M}{(2R)^2}$
$F = \frac{G~M^2}{4R^2}$
The magnitude of their gravitational force of attraction is $\frac{G~M^2}{4R^2}$.
