Answer
11.5 miles
Work Step by Step
To find a route whose distance is less than 12 miles, it will suffice that we simply travel from the closest to the furthest location, directly, forming a movement path that looks efficient.
Home → Bank is 1 mile.
Bank → Post Office is 1.5 miles.
Post Office → Dry Cleaners is 5 miles.
Dry Cleaners → Home is 4 miles.
This makes a total of $1+1.5+5+4=11.5$ miles.
(There are other paths shorter than 12 miles that are also easy to find)
