Answer
The rolling quarter makes 2 revolutions.
Work Step by Step
In a rolling motion, like the case of a wheel, the distance traveled by the axle of the wheel - which is at its center - equals the circular arc length at the edge of the wheel.
A similar situation here: the distance traveled by the center of the rolling quarter - the circumference of the black circle - equals the total circular arc length at the edge of the quarter.
If we take the radius of a quarter to be $R$, the black circle's radius is $R+R=2R$, so its circumference is $C=2R\times2\pi=4\pi R$
Therefore, the total circular arc length traveled at the outer edge of the quarter is $4\pi R$
Now 1 revolution of the rolling quarter equals a circular arc length of $2\pi R$. Therefore, the number of revolutions the quarter makes is $$\frac{4\pi R}{2\pi R}=2$$
