(a) Find the gravitational force exerted by the Moon on a 70.0-kg man at the Earth’s equator at noon.?

The acceleration due to gravity on the surface of the Moon = 1.625 m/s²

Gravitational force exerted by the Moon = m g = 70.0 × 1.625 = 114 N

"Noon" is relative to where the sun is in the sky. The problem asks about the Moon's force, but does not say where the Moon is. The sun's location is irrelevant.

The force from the moon might be 2.02 milli-Newtons, or 2.52 milli-Newtons, depending on where the Moon is. That's about 306,000 times less than the force from the Earth. A breath of air is over 10 times more.

F = G m1 m2 / r^2 

m1= masses of the moon
m2 = mass of the man 

r = distance between man and Moon's centre (distance between Earth and Moon)
replace it with numbers and get the magnitude gravitational force

The Moon, being a sphere, behaves like a point mass at its center in terms of the gravity objects above its surface experience.

F = G m1 m2 / r^2
m1, m2 = masses of Moon and man
r = distance between man and Moon's centre (effectively distance between Earth and Moon)