How did Kakashi get mangekyo sharingan?

Answer 1

Manga never stated how Kakashi got his Mangekyo Sharingan. So it is still unknown how he got it unless it will be shown in future chapter/episodes. Below are fan based theories-

Itachi told Sasuke that the only (known) way is to kill the closest person to you, that's how Itachi got his, and that's also how Sasuke got his. Kakashi obtained it in a different, unknown way......

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The impact of losing someone really close to you is what activates the Mangekyou

Even though Sharingan is a Kekkei genkai, KAKASHI had it planted in him so he's got all the ability to perform any sharingan justu. the only problem is that his body can't handle it since he doesn't have that unique chakra of the Uchiha.

Kakashi awakened his Mangekyou by seeing through its activation when he fought Itachi. When itachi used the Tsukuyomi, kakashi was able to see through and understand the "psyche" of the Mangekyou.

And as for the shape of kakashi's being different...everybody's Mangekyou has a unique shape, i believe.

Sasuke's was awaken through the death of his brother, not Ochimaru. After Madara reveals how Itachi tried to protect him and was used by Konoha to sacrafice the Uchia clan, he realizes how important and loving his brother was to him, and this awakens his mangekyo sharingan. Previously it was transferred at the end of the fight between itachi and sasuke, and this was just another effort for Itachi to protect his brother. After Sasuke's is awakened, Itachi's transfered mangekyo is never shown again.

Madara received the ETERNAL MANGEKYO by taking his brothers eyes, this gives the "new light" the the mangekyo is constantly searching for and stops the eye from going blind. It has nothing to do with the death of someone close, it can only be transferred between siblings, and both must already occupy the mangekyo. Later in the manga around episode 490 Sasuke does decide to accept Itachi's eyes only so that he can defeat Naruto who has mastered Sage mode, and he wants to defeat him with the full power of the mangekyo.

As for Kakashi no one knows how he got his, since everyone close to him was already dead. The most logcal is through hand seals, as well as understanding how to activate it after Itachi used it on him.

Answer 2

Kakashi awakened his Mangekyou Sharingan not long after receiving the new eye from Obito. Obito explained that after Madara had found him, and healed him enough to be able to fight, he escaped from his cave because he sensed Kakashi and Rin were in danger.

However when he got there, he saw Rin died, Kakashi's hand piercing her chest, a victim of his Chidori move. At that moment, Kakashi's eye switched to its Mangekyou form, as did the eye that remained in Obito.

The reason behind the killing has not yet been explained though.