A batter gets a hit when he reaches a base without getting out or forcing another runner to get out.
When a batter gets a hit, how does the scoreboard show that?
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The simple answer is "it doesn't", at least not the scoreboard you're showing there. This doesn't actually matter, because hits don't win games, runs do.
If you look at the box score for a game, you will see that the hits by each player are broken out. Copying from the example on the Wikipedia page and looking at the "h"its column
Atlanta Braves ab r h rbi bb so po a Smith dh 3 1 0 0 1 0 0 0 Pendleton 3b 5 1 4 2 0 0 1 2 <more players>
shows that Smith didn't get a hit in that match, but Pendleton got four hits. Similarly, expanded scoreboards at the games will sometimes show things like "4-5" to indicate that Pendleton had 4 hits in 5 at bats.