In what ratio the mass 4m should be split so the value of gravitational force comes maximum for a fix distance d between the masses?

F=G (4m-x) / r^2 G/r^2 (4m-x^2)

Let mass 4m be Z

F=G (m1 * (Z-m1) / d^2

Using calculus ...

dF/dm1=0=G (Z-m1) / d^2 - m1/d^2)

solving for m1,

Z-m1-m1=0

m1=Z/2

So split into 2m, and2m.

Now if you don't know the wonderful world of calculus, then plot the following parabola, and see where it is max:

F=G (m1 * (Z-m1) / d^2

k=Z (m1) - (m1) ^2