Find and destroy termite mounds is a mission in Daxter. After the mission "Take out bug in Emerald Isle", Ximon relayed a message to Daxter from Osmo to return to the construction site. Upon arrival, Osmo told him he had to destroy a collection of termite mounds before the site's management would turn on the exit elevator.
Upon arrival you must first head through an area of the construction site in which you do not encounter enemies until you reach an elevator. After exiting, Osmo calls you and the mission will begin. For now the path forward is fairly linear. Use pallets with bricks held up by cranes, trampolines and climbable walls to make your way through the site. Shortly on you must heat up giant springs that rotate and allow you to use an attached piece of metal as an extension to gain some extra reach when hovering. Also beware of metal creepers infesting some walls; keep note that they deal double damage on these vertical areas.
After another elevator you enter a small but relatively open area in which you can find the four termite mounds. They repeatedly spawn termites but are vulnerable to the flamethrower attachment. The first mound is right in front of the elevator. A second is at the end of the passage to the left. A third in a separate room to the right, use a small opening in the wall to get there. The fourth and last termite mound is to the right of the exit elevator.
Said elevator does not lead directly to the exit however. Instead, proceed to fight several more bugs and engage in a few more platforming sections until you reach a rail from which you can zip down and return to the streets.