transistor voltage amplifier question
Here's a  hint.

Imagine V1 is 2 V. The transistor's emitter is 0.7 V lower than the base voltage, so it is at 1.3 V. A current I = 1.3/Re flows. This same current flows through the collector (ignoring beta effects). So the collector voltage is 12 V - I*1k.  Now, if V1 increases to 3 V, the emitter will increase to 2.3 V, and I will increase to I_new = 2.3/Re, and the collector will decrease to 12 - I_new*1k.

The gain is the change in collector voltage divided by the change in emitter voltage.