What system allows multiple computers and their peripheral devices to be connected over a distance?

The system that allows multiple computers and their peripheral devices to be connected over a distance is a network. A network facilitates communication between computers and enables them to share resources such as files, printers, and internet connections. This can be accomplished through various configurations, such as local area networks (LANs) for short distances or wide area networks (WANs) for longer distances. Networks can operate using different technologies, including wired connections (such as Ethernet) and wireless connections (like Wi-Fi).

The other options, while related to computing, do not provide the functionality described in the question. A database is primarily focused on storing and managing data, a framework typically refers to a structure that supports the development of applications, and an operating system manages computer hardware and software resources but does not inherently provide the capability to connect multiple computers together for resource sharing over a distance. Thus, the concept of a network is essential for creating interconnected systems that facilitate collaboration and resource sharing among multiple devices.