ANSWER:

Allah is capable of doing everything as He is the creator of the Heavens and the earth.

However, this relates to the possible and not the impossible. 

If someone says: Can Allah create something he can’t move? We say that this is a stupid question! If Allah created it, Allah can move it. But the essence of your question is originally not correct and it is not this. 

Your question is: Can Allah be incapable of doing something? This is not possible!

I wanted to ask you how to answer the following question in the most logic and easy way: Can Allah create a stone which he himself cannot lift? Could that be the answer: Yes he CAN. But he doesn’t do it because he doesn’t do ungodly things therefore he doesn’t loose his almighty power? Please answer both.