Blue Lines are the COLD water .......white braided line comes from pump discharge and feeds cold water system. City water ties into cold line
The two connections are on the Water Heater
Cold (Blue) goes in bottom of WH Tank
Hot (Brown?) comes out top of WH Tank
The valve on blue line is the cold inlet/bypass valve for WH
If leak is from either cold/hot fitting (black connectors) they should seal up when tightened---hand tightening should be enough or just a little snug up with pliers. Not too much or you can crack fitting
May have to unscrew and check that seal inside fitting is not cut/torn
If leak is from either cold/hot 'nipple' (sliver) they should seal up with tightening using channel locks or small pipe wrench. Caution.they are threaded into an Aluminum tank with aluminum threads
If leak is from connections on 'Ells'/'Ts' where the 'bands' are used...those are PEX Crimp Rings. Special tool used to 'crimp' them closed.
Usually have to replace vs tighten.