The wiring was cut on my riding lawn mower, it has a troy bilt engine and I don't know where the black wire goes, I connected the red to red and the orange to orange but it has a purple wire and a white wire coming from the mower and a black wire from the engine, help

Hi,
Black wires are most certainly so form of ground. The other two depend on the model, which you did not give.
Peace,
Clarke