1 sn The proverb provides a contrast between God and the king, and therein is the clue to the range of application involved. The interest of the king is ruling or administering his government; and so the subject matter is a contrast to the way God rules his kingdom.
2 sn The two infinitives form the heart of the contrast – “to conceal a matter” and “to search out a matter.” God’s government of the universe is beyond human understanding – humans cannot begin to fathom the intentions and operations of it. But it is the glory of kings to search out matters and make them intelligible to the people. Human government cannot claim divine secrecy; kings have to study and investigate everything before making a decision, even divine government as far as possible. But kings who rule as God’s representatives must also try to represent his will in human affairs – they must even inquire after God to find his will. This is their glorious nature and responsibility. For more general information on vv. 2-27, see G. E. Bryce, “Another Wisdom ‘Book’ in Proverbs,” JBL 91 (1972): 145-57.