Albaby, is there nothing you don't already know about or can suss out by a keen google search in a few minutes?

You'll make me blush!

However, your post is Greek to me.

Oh, sorry. Here's a slightly more detailed explanation:

Generally speaking, in partisan races with multiple parties, each party get to choose their own nominee. So if there's a Democratic party, a Republican party, and an Albabian party, each of those parties get to nominate someone. When all three parties nominate their own separate candidates, you end up with three lines on the ballot with three different people.

In most states, you cannot seek the nomination of more than one party in the same race. If you're the Democratic party nominee, you can't also be the Albabian party nominee - and vice versa. So the same person would never appear in multiple ballot lines, since appearing as the nominee for one party would preclude being the candidate for another party.

In New York and a few other states, though, you can seek the nomination of more than one party. If you successfully get nominated by more than one party, you will appear as the candidate for more than one party.

So some of the candidates on your ballot were able to get the nomination from two parties - and the judicial candidates appear to have secured the nomination of all the parties (presumably because there were no other material candidates).