Final answer:
The run-on sentence is 'Please help me wash him, he's dirty.' It improperly joins two independent clauses without the correct punctuation or a coordinating conjunction.
Step-by-step explanation:
The example of a run-on sentence in the provided options is 'Please help me wash him, he's dirty.' This sentence has two independent clauses 'Please help me wash him' and 'he's dirty' that are incorrectly joined without proper punctuation like a period, a semicolon, or a comma with a coordinating conjunction. To correct this run-on sentence, you could write 'Please help me wash him; he's dirty.' or 'Please help me wash him, for he's dirty.' or even divide it into two separate sentences: 'Please help me wash him. He's dirty.'