Explain Plato's metaphysical idealism in The Republic X ?
This is a very interesting question. Towards the end of the book, Plato talks about the myth of Er. Er is a warrior who dies in battle, but he actually finds out that there is life after death. He is whisked away into heaven and he is given the ability to observe what happens within in this eschatological system. He is given this ability to report back to the people what the afterlife holds. He is a messenger of sorts.
In short, good deeds (virtue and wisdom) are awarded and bad deeds are punished. This takes place for 1000 years either in heaven or hell. After the 1000 years, all the people come together into a common place and they are given the choice of their new life (another cycle). Those who lived life of virtue will choose well; the others will not. More particularly, it is the life of philosophy that allows a person to choose in life and the afterlife the best paths.
Based on this discussion, idealism can be seen in the emphasis on the importance of the mind. Moreover, it can be noted that Plato's eschatology is immaterial.