If you use emt and ends are properly bonded to panel, you only need three conductors. Two blk or red #6 and a white #8 for a neutral, your conduit carries ground. Just make sure the green bond screw in sub-panel is removed and thrown away to ensure that neutral does not contact grounds in sub. I myself would use pvc and add a #8 green for a ground. This will make job go twice as fast and save money. But I would further save by using aluminum and that would be about half. You would need two #4 hot and a #6 neutral and ground could be a 6 also. Thats just a workin mans opinion, sorry to bore you, good luck......
See my work-Check out my album. "Git 'Er Done":D