Take a look at the original sentence again:
Richard squeezed, thumped, and shook the empty shampoo bottle, hoping for
a few drops to wash his dirty hair, since
the bottle was completely empty, Richard worked up a lather with a few sprinkles
of bathroom cleanser instead.
You wanted to fix it this way:
Richard squeezed, thumped, and shook the empty shampoo bottle, hoping for
a few drops to wash his dirty hair since
the bottle was completely empty, Richard worked up a lather with a few sprinkles
of bathroom cleanser instead.
To delete the comma between hair and because would cause an equally bad problem, a fused sentence. A fused sentence occurs when you have two complete sentences joined with no punctuation whatsoever. Richard squeezed, thumped, and shook the empty shampoo bottle ... begins the first sentence. Since the bottle was completely empty, Richard worked up a lather ... starts the second sentence. The spot between hair and because needs a stronger break than blank space.
You might want to consult the rules for fixing comma splices and fused sentences.
Go back to the sentence to try again.