The distance around the full circle is 75 inches. Call this distance C (for circumference)
We only want a small piece or fraction of the circumference. That piece is marked in blue in the diagram. It's known as an arc.
To find the length of that arc, we multiply the circumference C by the fraction 72/360. The first part (72) is the measure of the central angle, or the arc measure. The second part 360 refers to the fact that there are 360 degrees in a full circle.
So we have
arc length = (72/360)*C
arc length = (72/360)*75
which is why the answer is choice C