On a 16 h briggs&stratton riding mower the wire is melted what two wires are needed to run and start the motor

A couple of things could cause that.
1. A bad ground.
2. A loose wire on the hot side or ground side
3. A bad ignition switch
4. The starter is going bad and pulling too much amperage when cranking. If it seems like the battery is a tad low too many times and seems to turn slowly and all other wiring has a clean bill of health then I suspect the starter is going bad.