Your forum profile says you use a version of SketchUp that does not exist:
In this case it matters, because SketchUp Make (available as 2017 only) does not include the Pro Solid Tools that could make this task easier.
Using Make you will need to select the faces of your board, right-click and select “Intersect Faces with …Model”, then hide the TTracks and clean up the excess edges and faces inside the slot for the track. Don’t explode the TTrack groups, as you don’t want their edges and faces to merge with the board as a mass of loose geometry, you just want to know where the TTrack faces intersect the board.
BTW, if would be better if you make the board a group or component too. Sooner or later you are going to get something sticking to it or disrupting it when you didn’t intend to.
Edit: actually @tweenulzeven’s idea is better. Sometimes I take a problem statement too literally…
Edit2: In this case, because the board starts out as a simple rectangular block, I’d suggest erasing all of it and starting over (that way you won’t have to deal with the mess of stuff currently inside the grooves). Draw the board and place the TTracks where you want them (are they supposed to stick above the surface like that?). Then trace the outline of a TTrack (just where it intersects the one end of the board), hide the TTrack, and pushpull the outline through the board to create the slot.