Objects 1 and 2 attract each other with a gravitational force
of 18.0 units. if the distance separating objects 1 and 2 is
changed to one-half the original value (i. e., halved), then the
new gravitational force will be units.

27unit

Explanation:

18×3/2= 9×3= 27unit

The new force will be 72.0 units.

Explanation:  The gravitational force between two objects can be written as:

F = G*m1*m2/r^2

Where G is the gravitational constant, m1 and m2 are the masses of both objects and r is the distance between them.

Now, we have that F = 18.0 units.

Now, supose that we change r to r/2, the new force is:

F' = G*m1*m2/(r/2)^2 = 4*G*m1*m2/r^2 = 4*F = 4*18.0 units = 72.0 units

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