The Moon Escape velocity is 2.38 km/s while on Earth it is 11.186 km/s.

Since energy is proportional to the square of the speed (E=1/2*m*v^2) we can conclude that it is (11.186/ 2.38)^2 = 2 time easier to reach free space from the Moon than from Earth.

However, even if a rock is launched from the Moon at 2.38 km/s, it still inherits the inertia of the Moon. Simply speaking, the rock would not fall to Earth. It would be in an orbit similar to the Moon orbit.

The orbital speed of the Moon is about 1km/s so the rock must be given that additional acceleration to cancel its orbital speed.

At that point, the rock is immobile (from the Earth point of view) and it will start falling toward Earth because of ... gravity.

When it reaches Earth, its speed will be equal to the Earth Escape velocity (a bit less in fact since the rock did not start falling from an infinite distance) so 11.186 km/s.

The kinetic energy is given by the formula 1/2 * m * V^2 so for 1kg the kinetic energy at 11km/s is 1/2 * 1 * 11000^2 = 60 * 10^6 Joules

As a comparison, 1kg of TNT provides 4 * 10^6 Joules so each kg of moon rock would be equivalent to approximatively 15kg of TNT

The Hiroshima bomb was 15 kilotons of TNT = 15 * 10^6 Kg so a similar effect would require a 1000 tons of Moon rock and the ability to accelerate that rock to a speed of 2.38+1 = 3.38 km/s.