Take another look at the sentence:

Latoya tried to concentrate on Dr. Lemon's dull art history lecture, but the darkened classroom and endless slide show soon had her dozing in her seat, Latoya knew that Beverly would poke her with a pencil if Dr. Lemon bothered to glance their way.

The comma between lecture and but is necessary. Latoya tried to concentrate on Dr. Lemon's dull art history lecture is a main clause. The darkened classroom and endless slide show soon had her dozing in her seat is another main clause. Connecting two main clauses with a comma and a coordinating conjunction like but is a perfectly legal move in writing.

Go back to the sentence to try again.

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