Final answer:
Henry II asked Thomas Becket to become Archbishop of Canterbury to enhance royal influence over the church, but Becket resisted this by defending ecclesiastical privileges. Louis IX was trained to rule with advice from manuscripts financed by Blanche of Castile. The Triennial Act, unrelated to Becket, required Parliament to meet triennially.
Step-by-step explanation:
The King, referring to Henry II of England, asked Thomas Becket to appoint him as Archbishop of Canterbury. Becket's role after appointment complicated his relationship with the King, eventually leading to Becket's martyrdom. The appointment was intended to solidify the King's influence over the church, but Becket began to defend ecclesiastical privileges against royal encroachments, which was not what Henry II had anticipated. As for advice, it was common in the medieval era for rulers like Louis IX to receive counsel on how to rule effectively, which sometimes came in the form of manuscripts outlining the virtues and responsibilities of a king, as was the case with the advice from Queen Blanche of Castile.
In contrast, the Triennial Act mentioned in the question is related to the English Parliament and mandated that Parliament must meet every three years even if not called by the Crown, but it has no direct connection to Becket or King Henry II.