The words "petition" and "request" mean the same thing. She probably used these words together as a way of speaking very formally and respectfully to the king. (See: [[rc://en/ta/man/translate/figs-doublet]])
# if I have found favor in the eyes of the king and if it pleases the king
In order to show respect to a king, people sometimes did not call him "you." This can be translated with the word "you" along with other words that show respect. AT: "if you are pleased with me, O King, and if it pleases you" (See: [[rc://en/ta/man/translate/figs-123person]])
# if I have found favor in the eyes of the king
"Find favor" is an idiom that means be approved of or that he is pleased with her. "In the eyes of the king" is a metaphor representing his evaluation. AT: "if the king evaluates me and approves" or "if the king is pleased with me" (See: [[rc://en/ta/man/translate/figs-idiom]] and [[rc://en/ta/man/translate/figs-metaphor]])
# let the king and Haman come
This can be translated with the word "you" along with other words that show respect. AT: "please come and bring Haman" or "please come and let Haman come with you" (See: [[rc://en/ta/man/translate/figs-123person]])
# I will answer the king's question
This can be translated with the word "you" along with other words that show respect. AT: "I will answer your question" (See: [[rc://en/ta/man/translate/figs-123person]])
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