Horizontal tangent lines happen when dy/dx= 0, so when 2t=0, so t=0. plugging t= 0 back to the x and y equations, x=0, y= -6, so (0, -6)

Vertical tangent lines happen when dy/dx is undefined, so when 3t^2-3, so when t= -1 and when t=1. plugging back to get x and y, we get (2,-5) and (-2, -5)