The question asks us to spot the one structure that does not belong to the extrinsic group of laryngeal attachments.
Think of the larynx as a box of cartilages. Anything that ties this box to a neighbour (the hyoid bone above or the trachea below) is extrinsic. Anything that ties two cartilages of the box to each other is intrinsic.
The thyrohyoid membrane reaches up from the thyroid cartilage to the hyoid bone, so it is extrinsic. The hyoepiglottic ligament holds the epiglottis to the hyoid, again reaching outside the box, so extrinsic. The cricotracheal ligament drops from the cricoid down to the trachea, so extrinsic as well.
The cricothyroid membrane sits entirely between the cricoid and the thyroid cartilage. Both ends are laryngeal cartilages, so it connects the box to itself. That makes it intrinsic, and it is the odd one out.
\[\boxed{\text{Cricothyroid}}\]