Think of light intensity from a bulb: when you move twice as far away from the lamp, the light spreads out over an area four times as large, making it four times dimmer ($1/r^2$ law).

Inverse Square: Double the distance, divide the force by four ($2^2 = 4$).

Universal Law of Gravitation states that every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is given by $F = \frac{G m_1 m_2}{r^2}$. If $r$ is replaced by $2r$, the new force $F'$ is $F' = \frac{G m_1 m_2}{(2r)^2} = \frac{G m_1 m_2}{4r^2} = \frac{F}{4}$.