Review the original item:
Bored with the lecture on comma splices and fused sentences, Jayson started
poking Kim with the sharp tip of his pencil finally
she whirled around, threatening to slug him if he interrupted her
learning one more time.
You chose the correct way to fix the error:
Bored with the lecture on comma splices and fused sentences, Jayson started
poking Kim with the sharp tip of his pencil;
finally, she
whirled around, threatening to slug him if he interrupted her learning one
more time.
Jayson started poking Kim with the sharp tip of his pencil is a main clause. She whirled around ... is a second main clause.
A semicolon is an excellent way to join two main clauses that are closely related in meaning.