A bullet of mass m hits a block of mass M elastically. The transfer of energy is the maximum, when :

In an elastic collision, if mass of the two colliding bodies are equal, then they exchange their velocities.
Here if the mass of the bullet and mass of the block, are same, then the bullet will come to rest, and block will move with the velocity of the bullet; hence, maximum kinetic energy will be transferred.
So, condition is M = m.