Double alkylation of benzene to form tetralin
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