A perfectly inelastic collision is one in which the two objects completely stick together. Momentum is conserved, but energy is not. We are told that the neutron and nucleus for a new element, which means they've stuck together.
In a perfectly elastic collision, on the other hand, they bounce off of each other, conserving both energy and momentum.
Most real collisions are actually somewhere in between, involving objects that bounce off of each other, conservation of momentum, and some loss of energy.