"He does not know how to read."
Translation:Он не умеет читать.
In Russian "знать как ..." only means "to know how to .." in the literal sense: to have knowledge/information about performing some action (OK, there is another use with perfective verbs, which I am not going to cover here). With skills an abilities, the verb «уметь» is used.
With physical possibility to do something in real world (even if not specified when and where exactly), you use мочь (я могу́, ты мо́жешь, он мо́жет and so on). Both with perfectives and imperfectives it is used in the meaning of it being possible for such thing to happen, to be done. For example, Я умею читать и писать, but Я не могу писать и читать одновременно (simultaneously)—at least, without losing some speed and precision. :) The first sentence means that reading and writing are both abilities that I possess. The second sentence means that it is not possible for me to simultaneously do "reading" and "writing" (without any drawbacks).
English happily uses "can" for both meanings.