The meaning may change depending on the contexts. But in general, It means he knows his own way of doing things. For example, - 'Can he find where we are? ''Oh yes, he's lived here for long time. He knows his way''' In this case, knowing the way literally means he knows the direction. or "Can your friend really fix my car?" "Yes. He's worked as a mechanic before. He knows his ways. Don't worry". Here, it'd mean he knows 'how to fix the car'. He knows how it can be done.

Hi Sinem! It means he knows the route, the path or has directions that will take him to his destination. We might say this when we are confident that someone will not get lost during the journey: A. (Worried) "What if he gets lost?" B. "Don't worry, he'll be fine. He knows his way." 'To know one's way around' means to be familiar with the place we are in. When I first moved to Barcelona, I found the maze of streets really confusing as they all looked the same. Now I know my way around pretty well. Hope this helps!