Episode 185

The Day of Days is 18th episode of Inuyasha the Final act

Plot
Kagome travels back to her time for her entrance exam as the others wait for Kohaku to wake up. As she realizes that no one is around (her family won a trip to a hot springs and there's no school because it's a Sunday), she falls asleep only to wake up to Inuyasha in her bedroom. He tries to make her stay in her own time until Naraku is defeated, but Kagome decides to keep fighting in the hopes that her powers (which were sealed by the jewel in response to Kikyo's first wish as she originally died to stop fighting)would come back. Inuyasha responds by promising to protect her with his life, and the two almost kiss until they are interrupted by Souta, since Kagome's family had just come back from their hot springs trip. After ten days, Kagome leaves home for her entrance exams, but Inuyasha, who is hell-bent on keeping his promise to her, follows. When Kagome accidentally leaves her bag on the train, Inuyasha gets it back for her, and she immediately hugs him for it (unfortunately, she leaves her ticket at home - but her mother saves the day and bring it to her).

Trvia

 * this episode shows Inuyasha and Kagome almost kiss