The Sidonian People's Action Party wins (2) seats, and The Worker's Party wins (1) seat.

Details:

With a valid poll of 14 voters, the Droop quota is the integer part of (14 ballots/(3 seats 1)) 1 == (4) votes to gain a seat.

The ballot totals for first choice are: NAO 3 votes, SPAP 6 votes, and TWP 5 votes.

The process for calculating the winners of an STV election is: Award seats to full quotas, eliminate parties below the threshold, reallocate eliminated parties' votes, repeat.

In round 1, TWP and SPAP have enough to make one quota each. They each "spend" (4) votes on a seat, leaving TWP with (1) unspent vote and SPAP with (2) unspent votes.

NAO, not having a full quota of (4) votes is eliminated from the running. All (3) NAO ballots go to their second choices: in this case all (3) chose SPAP as their second choice so these ballots become SPAP votes.

In round 2, unused ballots are SPAP (5) votes, TWP (1 vote). SPAP has made another quota, so the third seat is theirs.

For a full explanation of what is going on here:

Sidon uses STV ballots to create a Proportional Representation (PR) parliament.

For an overview of what STV is, see this video.

For a detailed sample STV election which explains almost exactly how Sidon elections work, watch this.

The last detail is that Sidon uses a "Droop quota" in its process, which is explained here.