Why You name a transistor stage by the element that is common to both the input and the output loops at signal frequency. In Figure E7-1 the signal enters at the base, leaves at the collector, and the emitter sits at AC ground (grounded directly or through a bypass capacitor), so the emitter is the common element. This configuration gives both voltage and current gain and inverts the signal 180 degrees.
Watch out Common collector and emitter follower are two names for the same circuit, so neither can be the answer here; in that circuit the output is taken from the emitter and the voltage gain is slightly less than one. A common base stage would drive the emitter and hold the base at AC ground.
Follow the output: from the collector = common emitter, from the emitter = follower. Also, two choices naming the same circuit are both wrong.