To Be Able To Do
intransitive verb, ichidan verb
When you exit and come, apparently it means to be able to do. I think of it like you're leaving a location (出) to do a task and then you come (来る) back after you did it. Perhaps you were waiting in a room training like someone from Dragonball. When you leave the room, you are ready to fight the enemy and win. You train in that room to be able to do whatever you need to do, and only leave and come back alive because you were able to do it.
できる
The readings are a bit strange. Both kun'yomi, where 出 is で and 来る is きる. This is different from the reading you learned with 来る (くる), though, so be careful. If you can remember that and remember the kun'yomi readings from the previous vocab, you should be able to learn this one's reading as well.
やっとJLPTN1にごうかくすることが出来ました。
I was finally able to pass JLPT N1.
ここまではできましたが、最後の問題が難しくて出来ませんでした。
I could do up to here, but the last question was really difficult and I couldn’t do it.
私は内面を美しくするために化粧品を食べました。あなたにもそれが出来ますか？
I ate my make-up to be pretty on the inside. Can you do that, too?