When does harry start to like harry in the half blood prince?

Answer 1

"When does Harry start to like Harry?"

Do you mean; When does Harry start to like Ginny?

It's pretty much throughout the whole book; he's jealous of Ginny's boyfriend(s).

They start going out in the end of the middle of the book.

Answer 2

Ginny Weasley. Ron's little sister. And Harry loved her too.

Answer 3

At the start of the Half-Blood Prince Bellatrix and Narcissa meet Snape, where Snape promises to protect Draco while he is doing tasks for Voldemort.