Kira and fake Kira are now fake boyfriend and girlfriend so that real Kira can use and abuse fake Kira’s Shinigami eyes to defeat L and bring about his future…
So Light puts his plan into action which means showing Misa his own Shinigami, Ryuk, and as he shows trust to her she tells him the way to kill a Shinigami. I’m pretty sure Rem told her not to tell anyone but there she goes babbling on about it anyway.
Unfortunately for Light she’s a lot more difficult then he thought. She might say that she’d do anything but that comes with restrictions. She wants date nights, for the dating side to be reality, and she really doesn’t want him seeing other girls. He wants to hide everything to make it harder to trace anything back to any one person but the thought of him dating other girls makes her jealous.
This gives Light a even bigger problem.
He thought he’d use Misa and dispose of her but instead he’s faced with the news that if anything shortens Misa’s lifespan then Rem will kill him too. As we know Light plans on living a long and healthy life as a god of sorts of his perfect world so death is a terrible thing for him. This means keeping Misa happy. It means having to keep her around. It also means that he’s got to look out for her and make sure NOTHING happens to her.
In the end he uses that to his advantage, having worked out that Rem obviously has feelings for Misa he asks Rem to kill L so that he was happy which would make Misa happy.
Again I felt like it was way too easy. Even if it takes a while because Rem needs to see L or whatever needs to happen Light himself would not have beaten L.
I mean how he got to this plan was extremely intelligent and he’s been backed into a corner for a few reasons, including the fact that L named Light his friend, his plans never go as planned and L see’s right through it.
One of those plans being another message from Fake Kira to the police.
L and Light are too similar, like L says, and it means that he has the slight edge. Whilst Light can think of as many plans as he wants its pretty certain that L will think around it.