Suppose earth were moved to a distance from the sun equal to 4 au. how much weaker would the sun's gravitational force on earth be? why?

Actual distance between earth and sun: 1 AU

Supposed distance: 4 AU

Given that the gravitational force is inverse to the square of the distance that separate the masses, this would be weaker if the distance is greater.

Here  you hava a mathematical demonstration:

Gravitational force α 1/r^2 (α is used to indicate proportionality)

Actual Force / [1 /(1AU)^2] = New Force / [1 / (4AU)^2]

=> New Force = [1 / 16 AU^2 ] * Actual Force / [1 / 1 AU^2]

New Force = Actual Force / 16

Then, the new force would be weaker; exactly it would be one sixteenth of the actual force.