Depends on direction of thrust and relative position of bodies

Firstly, the Earth-Moon system will definitely be disturbed. The most likely scenario is ejection of the moon, though collision is possible if you happen to... well, accelerate the Earth into the Moon. Theoritically it might also be possible to keep the Moon, but its orbit will be drastically changed.

You are applying the force to Earth only, which means that you are disturbing the parent-satelite system by adding an external force to one of the bodies only. If you wanted to keep the Moon in current orbit, you'd need to accelerate the system as a whole. Otherwise you are changing the relative velocity of the two bodies. As a simplification that might be easier to imagine - accelerating the Earth by X km/s in a particular direction should effectively be the same as accelerating the Moon by x km/s in the opposite direction - what matters is the relative change in velocity.

As you're accelerating the Earth (by your calculations) to 42km/s that means about 12km/s increase in speed over 12 hours. With a Moon orbital velocity of about 1km/s that change means that Moon's velocity with regards to Earth is anywhere from 13km/s (well over Earth escape velocity) to 11km/s retrograde (Moon's orbit is reversed). That "technically" leaves the possibility of the Moon not being ejected, as Earth's escape velocity is about 11.19km/s which gives a very slight margin of possibility. With that said, even if that orbit was somehow stable it would likely be very eccentric, with the possibility of periapsis lower than Earth's radius (although it seems to me that the Moon's apoapsis will increase rather than periapsis decreasing, depends on the specifics of direction of the acceleration of Earth), which can mean an imminent collision.

If the apoapsis will increase instead then you have a moon in a highly eccentric reversed (retrograde) orbit with a periapsis roughly the height of its former orbit, with a very high apoapsis and all the tidal consequences that come with it.

And of course accelerating directly into the Moon (which will move about 1/60th of its original orbit over the course of Earth's acceleration) will also lead to a collision.

Depends on direction of thrust and relative position of bodies

Firstly, the Earth-Moon system will definitely be disturbed. The most likely scenario is ejection of the moon, though collision is possible if you happen to... well, accelerate the Earth into the Moon.

You are applying the force to Earth only, which means that you are disturbing the parent-satelite system by adding an external force to one of the bodies only. If you wanted to keep the Moon in current orbit, you'd need to accelerate the system as a whole. Otherwise you are changing the relative velocity of the two bodies. As a simplification that might be easier to imagine - accelerating the Earth by X km/s in a particular direction should effectively be the same as accelerating the Moon by x km/s in the opposite direction - what matters is the relative change in velocity.

As you're accelerating the Earth (by your calculations) to 42km/s that means about 12km/s increase in speed over 12 hours. With a Moon orbital velocity of about 1km/s that change means that Moon's velocity with regards to Earth is anywhere from 13km/s (well over Earth escape velocity) to 11km/s retrograde (Moon's orbit is reversed). EDIT: Correction regarding escape velocities. At the escape velocity of the Moon from its current orbit would be about √2*current orbital velocity. Which will be about 1.44km/s. Hence, the Moon will be ejected.

And of course accelerating directly into the Moon (which will move about 1/60th of its original orbit over the course of Earth's acceleration) will also lead to a collision.