6 polys... done! Some 80 poly trees. Seriously though, your professor is smoking crack. No one goes that low, unless they are only seen from a long distance. 600 to 3000 is more like it.
Making trees at 60 triangles is definitely possible. These ones range from (IIRC) 6 to 75 or so triangles. As for gothic stuff... a dead tree trunk with a lot of dead branches. you model the trunk and some very rudimentary thick branches, and then add a lot of small stuff in with planes. A weeping willow might work well…