The mistake the student made is:
Did not find the longest chain; it should be decane.
In the name "3-butyloctane," it implies that there's a four-carbon butyl group attached to an eight-carbon chain (octane), which indicates an incorrect chain length consideration. The longest continuous carbon chain including the butyl group is likely to be longer than eight carbons, leading to a naming convention that suggests it should be based on a decane (10-carbon) chain instead.