The synthesis of 1-phenylprop-1-ene from propiophenone
This can be done it 2 simple steps. You are not adding to the carbon count so all you need to do is operate on propiophenone. 

Step 1 - reduce the carbonyl group to a secondary alcohol. Sodium borohydride in $\ce{MeOH}$ or $\ce{EtOH}$ will do this in high yield and the workup is straightforward.

Step 2 - dehydrate the secondary alcohol to give the double bond. As it is a benzylic alcohol, protonation of the $\ce{-OH}$ group and formation of the benzylic cation is strongly favoured and will give you the alkene you want. Catalytic para-toluenesulfonic acid in refluxing toluene (with water removal by Dean-Stark apparatus) will do this easily.