You are 20 degrees S and 35 degrees E and move to a new location which is 35 degrees N and 65 degrees W. What is your new location?

Imagine a coordinate system (an xy graph) where the positive y axis points North, the negative y axis points South, the positive x axis points East and the negative x axis points West. 

Your initial position is 20 South and 35 East. This is equivalent to the (x,y) point of (35,-20). 

You then move 35 North and 65 West. This is equivalent to moving +35 in the y direction and -65 in the x direction. 

Your new y-coordinate is thus (-20+35)=y=15.

Your new x-coordinate is thus (35-65)=x=-30.

Now we must assign the directions to your coordinate. If we look back at our initial definition of the axes, y greater than zero is North and x less than zero is West. 

So your final position is 15 North and 30 West.