Question

Calculate the acceleration of the moon towards earths centre

Answer 1

A=-(G*m^2)/r

Where
a = acceleration from gravity
G = A constant number*
m = mass of the object (earth or moon)
r = distance from the center of mass of the object
The negative sign is there to indicate that the force goes toward the center of mass.
Thanks to @aloofarjun for the edit.

Answer 2

1.620m/s square
This is due to gravity