Double alkylation of benzene to form tetralin I have been asked to suggest a synthesis for the following compound (tetralin) from benzene:



I am unsure how to do this. It surely can't be Friedel–Crafts alkylation because of carbocation rearrangement and polyalkylation, right? Possibly a double acylation followed by a double reduction? Is there an issue with this; maybe a competing aldol type reaction in the double acyl chloride reagent that would be required.
You've got it right, double acylation and double reduction - but the first reduction occurs after the first acylation.  FWIW, the name of the reaction is the Haworth reaction and is commonly used to synthesize substituted tetralins, naphthalenes and higher aromatic polycyclics.

In your particular case, here is a diagram of the first 3 steps in the reaction




Friedel-Crafts acylation of benzene with succinic anhydride
reduction of the ketone using a Wolff-Kishner or Clemmensen reduction
a second Friedel-Crafts acylation using strong acid; it is an internal cyclization and forms the needed ring
and finally (not shown in the above diagram) a second Wolff-Kishner or Clemmensen reduction of the resultant tetralone to produce the desired tetralin