During a solar eclipse,the moon(of mass 7.36x10^22kg), Earth(of mass 5.98x10^24kg), and Sun(of mass 1.99x10^24) lie on the same line,with the moon...

We use the the relation of law of universal gravitational law of Newton to find the force between the two bodies of mass M and m sepated by a distance R.

F= GMm/R^2, G is the gravitational constant, M and m are the masses of the bodies.

Between Earth and sun:

M= mass of sun =1.99x10^30 kg), m=mass of earth= 5.98x10^24kg) and R = 1.496 x 10^11 m, G=6.673 x 10^-11 N times m^2/ kg^2,

F = (6.673 x 10^-11 N times m^2/ kg^2,)(1.99x10^30 kg)(5.98x10^24kg)/(1.496 x 10^11 m)^2

= 3.54233552*10^22 N  is the force between earth and sun.

Between moon and sun:

M = sun's mass above, m = moon's mass = 7.36x10^22kg and R = Sun moon distance = Earth sun distance - Earth moon distance as both sun and moon and earth are on the same line= 1.496 x 10^11 m. - 3.84 x 10^8 m = 1.49214*10^11 meter.

F= (6.673 x 10^-11*1.99x10^30 *7.36x10^22)/(1.49214*10^11)^2

=4.38968*10^20 N is the force between sun and moon.

Between earth and moon:

F = (6.673 x 10^-11*5.98x10^24*7.36x10^22)/(3.84 x 10^8)^2

=1.991763064*10^20 N is gravitational force between earth and the moon.

The gravitational force exerted by sun on earth is 3.54233552*10^22 N  towards sun as calulated earlier and by same magnitude the earth exerts the force on sun , but towards earth.

Note:

(You did not provide the mass of the sun correctly. It should be 1.99*10^30 kg  and not 1.99*10^24 Kg  which is less than earth!).