How does Lady Macbeth’s understanding of Macbeth’s character help her to manipulate him to carry out the murder of King Duncan?
When Lady Macbeth first reads Macbeth's letter, she initially fears that he is "too full o' th' milk of human kindness" to take the fastest route to the throne of Scotland (1.5.17). She knows that he is compassionate and kind, and she is concerned that these qualities -- qualities they would have considered to be somewhat womanish -- will get in her way. This is why she wishes to have any semblance of these qualities removed from her own self, why she wishes to be "unsex[ed]" (1.5.48).
After Macbeth decides that he no longer wishes to murder the king, he tells his wife that they "will proceed no further in this business" (1.7.34). Because she has such a developed understanding of his character, she seems to know that wounding his pride will be the best way to get him to recommit to their plan. Therefore, she accuses him of being "green and pale" and suggests that he will have to think of himself as a "coward" forever if he refuses to go through with it (1.7.41, 1.7.47). She goes even further, saying that he was "a man" only when he promised to commit the murder, implying that he is no longer and can only be so again by going ahead with the plan (1.7.56). She insults his manhood and seriously wounds his pride when she says that she would sooner kill her child if she'd sworn to do so than renege on a promise. This is his tipping point; he cannot abide feeling as though his wife is more of a man than he. Because of her deep knowledge of his character, she knows precisely what buttons to push to get him to do exactly what she wants. For now.