Here is the sentence again:
Hoping to relax after a busy week at work and school, Cheryl smoothed on
some sunscreen, settled onto her pool raft, and opened her new Stephen King
novel, then her neighbor cranked up the
lawnmower, ruining the quiet.
The comma between novel and then is joining two main clauses. This construction, called a comma splice, is illegal in writing.
To fix the problem, you could put a period after novel and then capitalize the T for then.