When Lucca enters the bar to meet with Solazo, the man behind the bar sticks a knife in his left hand and a man begins to strangle him from behind. As Lucca sinks to the floor the knife is now stuck in his right hand.
I think you are wrong. If you notice in the movie, Luca Brasi won't shake hands with Sollozzo to seal the deal for him to betray the Corleone family. He then puts both hands down on the bar. Bruno Tattaglia then grabs Luca's left hand, while Sollozzo grabs Luca's right hand, stabbing it. A hitmen then chokes Luca from behind. So when Luca falls, it is his right hand that is stuck to the bar.
....definately his left hand. chalks2wmu is correct. Tattaglia holds Luca Brasi's right and the knife goes into his left. As Luca is being garotted the shot is taken at Tattaglia's right shoulder. When the camera cuts back from the face of Sollotzo the kinfe is quite clearly still in Luca's left hand.
I have just watched this scene carefully, several times, and it is perfectly clear that the bartender holds down Brasi's left hand while Sollozzo stabs Brasi's right hand. There is no slip-up.
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