First, it often helps to draw a picture to visualize these problems. In order to do this, I'd draw a basic graph. Make base camp your origin (0,0). Now your initial location is 80 m below base camp or -80 on your y-axis. Now you increase your elevation by 42, so you go up by 42 on your y-axis. In other words, you get the equation -80+42 or -38.
Now consider what the negative means on your answer. Since a negative value is below the origin on your graph, this means that you are now 38 m below base camp.
