Final answer:
Lynne should attempt to flash the latest firmware for her router as a first step to resolve the issue of her 3TB external USB hard drive not being recognized by the network. This action, recommended by the router manufacturer, may solve the problem by updating the router's software, improving compatibility with newer hardware.
Step-by-step explanation:
Lynne is facing an issue with her 3TB external USB hard drive not showing up on the network when connected to her router. Since the router manufacturer states that it can recognize drives up to 4TB, it's less likely that Lynne's hard drive's capacity is the issue. Instead, the solution could be related to the router's capability to properly communicate with the hard drive.
One of the first troubleshooting steps Lynne should take is to flash the latest firmware for her router. Firmware is the software that is embedded into the hardware device—in this case, the router—which controls how the device behaves. Manufacturers often release firmware updates to fix bugs and add new features. An outdated firmware could lead to compatibility issues with newer hardware, such as Lynne's 3TB hard drive.
Flashing the router with the latest firmware may resolve the issue and allow the drive to be recognized by the network. It's important for Lynne to follow the manufacturer's instructions carefully when updating firmware to avoid any potential problems. If updating the firmware does not solve the problem, Lynne could also check for any hardware drivers specific to her USB drive that might need to be updated, although this is less common for external USB drives.