4 sn The motives or plans of a person are “difficult to fathom”; it takes someone with understanding to discover and surface them (the verb in the last colon continues the figure with the sense of bringing the plans to the surface and sorting them out).
2 sn A fathom is about 6 feet or just under 2 meters (originally the length of a man’s outstretched arms). This was a nautical technical term for measuring the depth of water. Here it was about 120 ft (36 m).
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.