You can start by looking on fanfiction.net. It has a vast collection of fanfiction stories, and you can easily search for 'Harry and Hermione sixth year' fanfiction there. Another good place is Archive of Our Own (AO3). It has a well - organized tagging system, so you should be able to find relevant stories quickly.
A popular 'Harry and Hermione sixth year fanfiction' is 'The Sixth Year Awakening'. It begins with Harry having a premonition about the year ahead and how Hermione is going to be an important part of it. As the story progresses, they explore the Forbidden Forest together more often, which is a bit different from the original books. They also study ancient magic together, which leads to some really cool magical revelations and a deeper connection between them.
One possible reason could be a misunderstanding. Maybe Hermione overhears something Harry says and misinterprets it. For example, if Harry is discussing some dangerous plan with Ron and Hermione thinks he's being reckless without considering her input, she might leave in anger. Another reason could be her own personal growth. She may feel that she needs to explore her own magical abilities further on her own and that Harry's presence is somehow holding her back in that regard.
Harry might be initially shocked. He's so used to having Hermione around that her sudden departure leaves him feeling lost. He might start doubting himself, thinking that he did something wrong. For example, he might replay all their recent interactions in his head, looking for signs that he upset her.
One great 'Harry Hermione sixth year fanfic' could be 'The Sixth Year Bond'. It delves deep into their relationship during that year, exploring how they grow closer as friends and face the challenges together. The author does a wonderful job of capturing their personalities and the Hogwarts atmosphere.
One common theme is the deepening of their friendship. As they are in their sixth year, they've been through a lot together and the fanfics often explore how this shared history makes their bond stronger.
One great 'Harry and Hermione in 4th year' fanfiction is 'The Fourth Year Adventure'. It delves into their relationship during that challenging year. They face new magical tasks together and support each other in a very heartwarming way. It also shows how Hermione helps Harry prepare for the Triwizard Tournament.
There might be a fanfiction where in their fourth year, Harry and Hermione go on a secret adventure related to the Dark Arts that they suspect is connected to Voldemort's return. Along the way, they face many challenges and have to rely on each other's strengths. Hermione's knowledge of spells and Harry's courage are put to the test, and this experience brings them closer together as friends and perhaps something more.
Harry Potter himself is still very popular. Fans often like to put him in new situations or relationships in fanfiction. For example, exploring his growth as a wizard and a leader during his sixth year in different ways than in the original story.
Some fanfictions might focus on Draco Malfoy's internal struggle during Harry's sixth year. He was under a lot of pressure to carry out Voldemort's tasks. In the fanfiction, we could see more of his emotions and how he might have considered changing sides. He could be secretly helping Harry in some small ways without the Death Eaters knowing.