Don't feel bad, that question is horribly worded.
Gene mutation is a confusing choice of words, it is not a specific thing.
First, down syndrome IS caused by a mutation, specifically a duplication. Trisomy itself is a mutation, but not caused by a mutation to a single gene, which could be what "gene mutation" is referring to. If so, it is just bad wording and the book answer is wrong. But trisomy itself can be caused by a mutation to a single gene so even then it is iffy.
The question is a "gotcha question" at best or just straight-up wrong at worst. "Which of the following statements about gene mutation is incorrect?" There is no right answer here: a mutation can cause all of these things, since we don't know what exactly is meant with "gene mutation".
At first is seems like all of the answers could be caused by mutations, but there is twisted logic to C being correct.
A mutation can change alleles, thus, it can change a dominate allele into a recessive and vice versa. What it can't do is change a dominate allele into a recessive one... wait that sounds insane, but it is technically true. It is a confusion of language; lets go a little deeper.
A mutation can turn one allele into another different allele...but, if you referring to the allele as in the defined allele and not the gene then a mutation cannot change it. A mutation can never make the blue eye allele as it is defined, recessive, it can however change the gene from blue eyes to brown eyes, thus making gene go from recessive to dominant and thus changing from a recessive allele to a dominate allele. Think of it this way, I can make steel change color by heating it but I can never change the color blue itself. So C could technically be incorrect but from a slightly different angle it is complexly possible, thus the questions is just bad.
Why textbooks often have sucky questions.
You run into this problem with textbooks a lot for two reason.
The people who write/edit textbooks rarely understand the subject and even when they kinda do, they often reuse and shuffle questions often changing key terms without understanding how it changes the question. this is done to create a new "edition" which they can sell again when they drop online support for the old edition.