Rat Problem is an Odd Job in Chapter 3, "Home Sweet Slum", in Final Fantasy VII Remake, taking place in the Sector 7 Slums. While Tifa Lockhart gives Cloud Strife a tour of the Sector 7 slums, the two talk to the item store owner, who has an issue with the doomrat and wererats eating items from his store.
Beating this quest is required to unlock "On the Prowl".
Follow the marker to the item store owner, and interact with him, and he will ask Cloud and Tifa to deal with the rat infestation. The green marker will then point to the next destination, located through an opening at the end of a small tunnel in the northern end of Sector 7. Pass through the tunnel to encounter a group of wererats, which can be defeated in a few physical hits. For Chadley's Report, consider using the Assess ability.
After defeating the four rats, Tifa may encourage Cloud to return to the item store, as no doomrats were encountered. However, after doing so, the item store owner will just ask them to return to the same spot. Doing this spawns doomrats, which are significantly more durable, and are best off being staggered first. As Tifa, use several combos with Unbridled Strength to give her Omnistrike, and when the rats are together, use Divekick to hit them all in an area-of-effect attack. As Cloud, use Focused Strike to stagger the rats, then lay into them with Punisher Mode activated, with spells, or with Braver.
After the doomrats are defeated, the option is presented to teleport back to the item store. The item store owner will then offer the Cleansing Materia, which can use curative spells, for 300 gil, as well as three hi-potions, for 100 gil each, in stock. Cleansing is a strong purchase, and hi-potions are always useful. After this, Wymer offers another quest.
Hard mode tips
Though this quest itself does not offer much, it is required to unlock "On the Prowl", where Tifa can earn a manuscript.
The doomrats will appear immediately, and have much more HP than before, as well as being more deadly. Equipping Tifa with HP Absorption Materia paired with Deadly Dodge Materia or Parry Materia can be effective both in dealing damage as well as healing Tifa in between her attacks (with no MP cost), and she can make use of character abilities to defeat them quickly. Cloud, meanwhile, can use Triple Slash as well as other powerful abilities, and while spells are effective, it is better to save the MP.