The angle of the track's inclination can be measured, and as the cart travels along the track a certain distance the corresponding total change in height is proportional to the total potential energy of the system. The small piece of cardboard is an indicator (just a little orthogonality symbol shape) of how far the cart has travelled.
The cart slides down the track, picking up speed. The string pulls tight and stretches the spring, as the front end of the cart pushes the small cardboard piece down the track. This piece will remain where the cart stopped moving forward. This will give the total distance the cart has travelled and (measuring the distance to the piece while holding the cart to the point where the string is tight but the spring is unstretched) the distance the spring was stretched.
From this information it is possible to show the total kinetic and potential energies equal, find the spring constant, or find the mass (all depending on other information such as prior measurement of the spring constant or knowledge of the mass).