...... tired Melissa is when she gets home from work, she always makes time to say goodnight to the children.*WhateverNo matter howHowever muchAlthough

The correct answer is "No matter how".

So the sentence should read: "No matter how tired Melissa is when she gets home from work, she always makes time to say goodnight to the children."

This is because "no matter how" is used to emphasize that the degree or extent of a situation does not affect or change a particular fact or outcome. In this case, regardless of how tired Melissa is, she always makes time to say goodnight to the children.