At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
First think broadly (conceptually). Which side of A do you think you would need a mass in order to produce a gravitational force on A which would counter act (balance) the gravitational forces on A caused by B and C?
Next you must calculate. I would analyze the forces acting on A with a free body diagram (you only are asked to find Fnet= 0 for particle A (that is what "no net gravitational force" is saying). Force of gravity on A caused by B is in the +y direction and the force of gravity on A caused by C is in the -x direction. You must create a gravitational force (by choosing where to place your D mass (4.00ma) that will simultaneously cancel our those two forces (hint: the force of gravity on A caused by D will have both x and y components).
Hope that helps.
Not the answer you are looking for? Search for more explanations.
you can treat the x and y component separately
the x force of the new mass will be 4m/x^2 (where x is its x coordinate)
this has to cancel the force from particle c (=3m/1.5^2) so you can solve for x
do the same for y