What is the meaning of "b'Orech Apayim Yefuteh Katzin"?
Rashi: As long as Hashem delays anger and does not collect [from sinners], they put their hearts to entice Him with Teshuvah and Tefilah.
Malbim: If the officer is angry at you, do not try to totally remove your sin, for 'if you seized much, you did not seize' (Rosh Hashanah 4b) (you will not gain from this). Rather, strive to delay his anger, lest he punish immediately - he will be enticed to consent.
Malbim (according to the metaphor): Hashem is enticed via Tefilah to delay anger. Afterwards he softens the power of Din via a soft tongue and supplications.
How does a soft tongue break a bone?
Gitin 68a: Ashmedai (king of the demons) was being taken to Shlomo. He rubbed against a tree and a house, and toppled them. He came to a widow's shack. She supplicated that he not rub against it. He bent away, and broke a bone.
Rashi: Prayer and supplications break the harshness of a decree.
Malbim: This is a Mashal from gluttonous beasts, which break bones with their tongues. So after [persuading the officer to delay punishment], with supplications, the harsh Midas ha'Din will be broken. Also refer to 25:15:1:3.