Two spheres have a gravitational force between them of 45 N. If the distance between the masses
is increased to 4.0 times its original distance, what
is the new force?

The new force is 2.8125 N

Explanation:

Newton’s Law of Universal Gravitation

Objects attract each other with a force that is proportional to their masses and inversely proportional to the square of the distance.  

Where:

m1 = mass of object 1

m2 = mass of object 2

r     = distance between the objects' center of masses

G   = gravitational constant: 6.67\cdot 10^{-11}~Nw*m^2/Kg^2

Suppose two spheres have a gravitational force between them of F = 45 N. Now increase the distance to r'=4r. The new force F' is:

Substituting the original value of the force:

F' = 2.8125 N

The new force is 2.8125 N