You need to review your class notes about momentum and center of mass ... specifically you want to know what happens to the motion of the center of mass.
If you do not have class notes on this, then you need to look it up.
Apart from that, you know how to do this problem ... you know how to find the initial momentum of the bomb right at the highest pint (just before it goes off) and you know how to find the momentum of one of the bits that comes off, both from the clues. If you are drawing a blank at this, then look through your class notes on "ballistics".
You know that you have to show some attempt to solve the problem. The stone is projected, so it is projectile motion. What do you know about such motions?
At the top of the trajectory, the stone explodes into two segments. The forces acting during the explosion are internal. What quantity conserves when only internal forces act in a system?