Hi Sidney123,
The key here is in the meaning of the word "exemplify." It means to serve as an example of illustration of something. With that in mind, we can see why A doesn't work. What was getting exemplified? The ideal of the philosopher-king. Who or what was exemplifying that ideal? Solon (or a ruler such as Solon).
A says that the Plato exemplified Solon. Neither part of this makes sense. Plato isn't exemplifying anything, and Solon, as a person, cannot be exemplified. (How can Plato serve as an example of Solon?)
In B, "as exemplifed by" adds detail to the ideal of the philosopher-king. Plato likes this ideal to the extent that it is exemplified by rulers such as Solon. Solon exemplifies, or provides an example of, the ideal of the philosopher-king.
I hope this helps!