Question

if an optic nerve of a mature frog is transected and half of the associated retina is destroyed,
the destroyed retina regenerates and then axons grow out from the complete retina and innervate
the optic tectum in the species - typical fashion
half of the optic tectum degenerates
half of the retinal ganglion cells degenerate
the destroyed retina regenerates and then axons grow out from the complete retina and innervate
the optic tectum in the species - typical fashion
the axons grow out from the retinal ganglion cells in the remaining half of the retina to targets
systematically distributed over the entire optic tectum.

Explanation:

When the optic nerve of a mature frog is transected and half of the associated retina is destroyed, the remaining retinal ganglion cells (from the undestroyed half) have the ability to regenerate axons. These axons grow out and innervate the optic tectum. The growth is not just to a corresponding half - but rather, the axons from the remaining half of the retina distribute systematically over the entire optic tectum. This is based on the concept of neural regeneration and target innervation in amphibians (frogs in this case). The destroyed retina does not regenerate in the way described in the first and fourth options (as it is half - destroyed and the key is the remaining half's axon growth). The optic tectum does not degenerate (so the second option is wrong), and the retinal ganglion cells in the remaining half do not degenerate (so the third option is wrong).

Answer:

the axons grow out from the retinal ganglion cells in the remaining half of the retina to targets systematically distributed over the entire optic tectum.