The diagram is fairly self-explanatory but a little extra information can’t hurt. In the diagram you can the see a single Kanji, 育. This Kanji has a general meaning of “to raise, to bring up”. This is just the general meaning however and when it comes to using this Kanji in some specific context, using the appropriate reading (Kun or On) is required.
The Kun reading of 育 is used when referring to the verb of bringing up something, just like in the sample sentence: “Is it possible for me to raise an animal?” For the moment, simply notice that the Kun reading is “soda” in that very situation.
The ON reading, on the other hand, is used when talking about education as a noun: “The government has been reforming education”. Notice how the ON reading differs from the Kun reading, the former being “soda” while the later is “Iku”.
Understanding that a Kanji is read differently (either Kun or On) is all that has to be understood for now. Keep in mind that a Kanji can have several Kun and On readings.