OBR defines the defensive stat "Number of double plays participated in" as something the official scorer needs to note.
Further, in 10.11 DOUBLE AND TRIPLE PLAYS
"The official scorer shall credit participation in a double play or triple play to each fielder who earns a putout or an assist when two or three players are put out between the time a pitch is delivered and the time the ball next becomes dead or is next in possession of the pitcher in a pitching position, unless an error or misplay intervenes between putouts."
"Rule 10.11 Comment: The official scorer shall credit a double play or triple play also if an appeal play after the ball is in possession of the pitcher results in an additional putout."
I believe the correct answer to your question would be that "6, 4 & 3" should all get credit for a DP in the example provided.
For those of you who have read this far, the official baseball rules (OBR) actually provide most of the answers to questions asked here. Our friends at MLB.com have them on their web site. It's a searchable PDF...
OBR Scoring Rules