If the Moon is brought closer to the Earth such that its distance from the Earth becomes half of the original distance, then the gravitational force of attraction between the Earth and the Moon would:

According to Newton's Universal Law of Gravitation, the gravitational force (F) between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers [1]. This relationship is expressed by the formula F = G(m1m2)/r², where G is the gravitational constant. Because the force follows an inverse-square law, any change in distance has a squared effect on the force [1]. If the distance between the Earth and the Moon is reduced to half (r/2), the new force becomes proportional to 1/(1/2)², which simplifies to 1/(1/4), or four times the original value. Consequently, halving the distance results in the gravitational attraction increasing to four times its original strength.

Sources

1. [1] https://pwg.gsfc.nasa.gov/stargaze/Sgravity.htm