Here is an argument for the generally accepted thesis that knowledge-how is different from knowledge-that. Knowledge-that comes has two poorer cousins, true-belief-that and justified-true-belief-that. Knowledge-how does not seem to have such cousins.
In fact, knowledge-how seems more akin to true belief or justified true belief than to knowledge-that. Actually, it is possible to have knowledge-how in an area where one only has true beliefs. Suppose Georgina has all the skills and true beliefs that an automotive mechanic needs to have, but has very little in the way of knowledge. In fact, she has acquired her true beliefs about automotive repair from a fake psychic who, in a series of drug induced trances, uttered lots and lots of noises that happened to sound just like a series of lecture on automotive repair. Furthermore, Georgina has never actually touched a car. However, completely by chance, lightning has induced in her brain all the structures and motor memories that an experienced car mechanic would have. I am inclined to say that Georgina knows how to fix cars. The evidence of know-how is reliable execution, and she can do that. Suppose Georgina fixes your car. One can still question whether she knew how to do it. But if she reliably fixes cars, and does so consciously, with the right beliefs about how to do it, then she knows how to fix cars, no matter what source she got her know-how from.