This is a good synthesis to know, because vinyl benzene is a good starting point for many synthesis problems you will encounter down the road.
An ethyl group can be added to benzene via Friedel-Crafts alkylation.
To add that alkene, we you will have to do some sort of elimination reaction. The easiest way to do this is via bromination. Free radical bromination (with NBS or Br2/hν) will add a bromine to the position of the most stable radical, which is the benzylic position (due to resonance).
Then adding a strong base like potassium tert-butoxide will do an E2 reaction to form the alkene.
