Moneywort, or creeping Jenny, is a shade- and moisture-loving perennial groundcover plant that is care-free once established. A mere 2-4 inches tall, moneywort grows rapidly and spreads by sending 2-foot-long creeping stems along the ground. The stems root themselves at every opportunity, producing a dense, low-growing mat. It is considered an invasive weed pest in many areas.
Trim moneywort mats down with a lawnmower if you feel that 2-4 inches is too tall. It doesn't matter how short you cut these plants--you can't hurt creeping Jenny. Even if you shear plants off at ground level, the smallest pieces of root left underground will rapidly shoot up as healthy plants.
Thin overcrowding creeping Jenny by pulling up individual plants. Just reach down into the mass of upright stems, grasp one and pull it out of the soil by its roots. Since each moneywort plant sends out runners which root themselves wherever they can, you'll undoubtedly be pulling up some of the rooted runners with it. This will make your task easier -- you'll be pulling up multiple plants, thereby thinning other areas up to 2 feet away from the mother plant at the same time. Don't worry if you think you've pulled too many--moneywort will replenish itself very quickly, replacing what you've removed.
Transplant pulled moneywort plants anywhere you want a new mass of them to grow, or destroy them. Don't leave piles of pulled plants lying around where they can reseed or even take root, producing potentially undesired offspring.
Pinch moneywort stems back only if you want the already thick mass to quickly become even denser. A single plant produces a mass of closely spaced stems, and each is an individual plant that has developed its own root system. Simply break stems off with your fingers to the desired height.