For Physics homework I was asked the following question:
Suppose you first walk 12 m in a direction 20 degrees west of north and then 20 m in a direction 40 degrees south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position?
The answer that I arrived at was "26.61 m 65 degrees south of west" using the component method, but I was marked incorrect, is there another way to do this question or did I make a mistake in the calculation?

You have the correct distance, but incorrect angle. Draw it out - you will see that the position to the south of the east-west line is less than the distance west from the north-south line, hence the angle is not 65 degrees south of west, but 90-65 = 35 degrees south of west. It's hard to describe, but if you draw it out you should understand why this is so.