How should I implement grid based movement

Brilliant thank you I’m looking at the Sokoban one right now and think I understand, the main movement is through a lerp between the start position and a new set end position with a line trace in front of the player to see if they can move or not.

I dont however understand where this math is for the line trace. I understand that this value from the select is then times by one hundred later on to make it the end location.

Why would it need to add this end location to the start though i dont understand either?