More than likely the old motion sensor was powered with black and white wire, and the red was a normally open switch that closes with the motion(turns on). The new sensor is just a normally open between the white and black wires. So you would take your input power black wire and attach that to the motion sensor black wire, and the output(path lights)black wires to the white wire. Then you would attach the input power white(neutral) to the path lights white wires. With this new motion sensor you are only switching the hot wires on/off with a motion switch no neutral(white wire) is needed to be attached to motion sensor for it to work.

Yo dawg, you got inflated inflation in yo inflation, so we inflated some more inflation fo yo inflation… some billionaire in their best Xzibit voice😂