He would be filled with a deep sense of grief. Naruto has always cared about Hinata, and her death would be like a part of him has been ripped away. He might isolate himself for a while, blaming himself for not being able to protect her. But eventually, he would use his pain as motivation to get stronger and fight against whatever caused her death.
Naruto's reaction could be complex. He would feel an overwhelming sadness, but also a burning determination. He might break down in tears, but then quickly compose himself and start planning his next move. His reaction would also depend on the circumstances of her death. If it was a heroic sacrifice, he might feel both proud and heartbroken at the same time.
He would be filled with rage. Naruto has a strong sense of justice and the fact that someone took Hinata away from him would fuel his anger. He would vow to find and punish whoever was responsible. He might even become reckless in his pursuit of vengeance, endangering himself and those around him. His friends would have to step in to try and bring him back to his senses.
He would feel a deep sense of guilt, thinking that if he had been stronger or more aware, he could have saved her. Naruto might also start to cherish the memories he had with Hinata more, and this could change his personality a bit, making him more somber at times. He would probably vow to protect the things that Hinata held dear, like her family and the village.
Naruto might be shocked at first. He could stand there frozen, unable to believe what he's seeing. His face would probably show a mix of confusion and hurt.
One possible plot reason could be for Naruto to experience a great loss that changes his character completely. Maybe it's part of a dark plot where the enemy is so powerful that they manage to kill Hinata right in front of Naruto. This would fuel his rage and determination to become even stronger and seek revenge. Another reason could be related to some sort of sacrifice. Hinata might sacrifice herself to save Naruto or someone else important, and Naruto has to deal with the guilt and grief of her death.
Hinata would be in shock. She'd probably freeze for a moment, unable to believe what she's seeing. Her eyes would be wide open in horror.
Hinata would probably be angry too. She might be angry at the circumstances that led to Naruto's death, whether it was an enemy or some other misfortune. She could direct her anger towards training harder, vowing to become stronger so that she can prevent such a tragedy from happening to others in the future.
She would be devastated. Hinata has deep feelings for Naruto. His death would likely cause her to go into a state of shock and disbelief at first. She might blame herself for not being strong enough to protect him.
He might be amazed. Naruto is used to his own world and seeing a fan - made interpretation like an AMV fanfiction would be like seeing a new side of his story.
Well, in some fanfictions, when Naruto sees Hinata in the waterfall setting, it could be a moment of sudden realization. He might finally notice her in a new light, perhaps seeing her beauty and the depth of her feelings for him more clearly. It could be a turning point where he starts to develop deeper romantic feelings for her.
At first, Naruto would be completely shocked. He has always seen Hinata as a loyal friend and someone who has deep feelings for him. So the idea of her betrayal would be hard to fathom. He might try to deny it at first.