What is the difference between using こと and かた in a sentence with できます and わかります?


e.g. はなすこと and はなしかた I am trying to learn about this grammar point for a test
![enter image description here](https://i.stack.imgur.com/7GnfX.jpg)

My notes for できます and わかります ![enter image description
here](https://i.stack.imgur.com/Rbbwd.jpg)




(1) こと nominalizes a verb, so はなすこと is "speaking".  
(~が)できます means "can (do)~", so you can say:  

> はなすことができます。I can do + speaking → I can speak.  
>  [日本語]{にほんご}をはなすことができます。I can do + speaking Japanese → I can speak Japanese.  
>

Likewise,  

> かんじをよむことができます。I can read kanji.  
>  すしをつくることができます。I can make sushi.  
>

* * *

(2) かた is "way of ~"/"how to", so はなしかた is "way of speaking"/"how to speak".  
(~が)わかります means "I know~"/"I understand~", so you can say:  

> はなしかたがわかります。I know + the way of speaking. → I know how to speak.  
>  [日本語]{にほんご}のはなしかたがわかります。I know + the way of speaking + of Japanese → I know
> how to speak Japanese.  
>

Likewise,  

> かんじのよみかたがわかります。I know how to read kanji.  
>  すしのつくりかたがわかります。I know how to make sushi.

